Chapter 2, “Lines and Angles”, from the NCERT Ganita Prakash (2026-27) Class 6 Mathematics textbook introduces points, lines, line segments and rays, and then builds up the idea of an angle, showing students how to compare, classify, measure and draw angles using a protractor. Below are complete, section-wise solutions to every “Figure It Out” exercise in the chapter.
Last Updated: September 23, 2026
2.1 Point, 2.2 Line Segment, 2.3 Line, 2.4 Ray — Figure It Out (Page 15-17)
Q1. Can you help Rihan and Sheetal find their answers? — Answer: Rihan is trying to draw lines through a single marked point, so he can draw an…
Answer: Rihan is trying to draw lines through a single marked point, so he can draw an infinite number of lines through that one point. Sheetal is trying to draw a line through two marked points, so she can draw only one line that passes through both of the points.
Q2. Name the line segments in the given figure. Which of the five marked points are on exactly one of the line segments? Which are on two of the line segments? — Answer: The line segments in the figure are LM, MP, PQ and QR.
Answer: The line segments in the figure are LM, MP, PQ and QR.
- Points L and R lie on exactly one line segment each.
- Points M, P and Q lie on two line segments each, since each of them is the shared end point of two adjacent segments.
Q3. Name the rays shown in Fig. 2.5. Is T the starting point of each of these rays? — Answer: The two rays shown are ray TA (starting at T and passing through A) and ray TB…
Answer: The two rays shown are ray TA (starting at T and passing through A) and ray TB (starting at T and passing through B). Yes, T is the starting point (the initial point) of both rays.
Q4. Draw a rough figure and write labels appropriately to illustrate each of the following — Answer:
Answer:
- (a) OP and OQ meet at O: Draw two line segments OP and OQ that start from the same point O and go off in different directions, meeting only at the common point O.
- (b) XY and PQ intersect at point M: Draw two straight lines, one through points X and Y and another through points P and Q, so that they cross each other at a single point, which is labelled M.
- (c) Line l contains points E and F but not point D: Draw a straight line l that passes through E and F, and mark point D somewhere away from the line, not touching it.
- (d) Point P lies on AB: Draw a line segment AB and mark a point P anywhere between A and B, on the segment itself.
Q5. In the figure, name (a) five points (b) a line (c) four rays (d) five line segments — Answer:
Answer:
- (a) Five points: D, E, O, C and B
- (b) One line: line DB
- (c) Four rays: OC, OB, EB and OD
- (d) Five line segments: DE, EO, OB, DO and EB
Q6. Here is a ray OA (Fig. 2.7). It starts at O and passes through the point A. It also passes through the point B — Answer:
Answer:
- (a) Can you also name it as OB? Why? Yes. A ray is named using its starting point followed by any other point that lies on it. Since the ray starts at O and B also lies on it in the same direction as A, the same ray can correctly be named OB as well as OA — both names describe the same ray.
- (b) Can we write OA as AO? Why or why not? No. OA denotes a ray that starts at O and extends through A, while AO would denote a ray that starts at A and extends through O — the opposite direction. Since the starting point of a ray must come first in its name, and the two rays point in opposite directions, OA and AO are not the same ray.
2.5 Angle — Figure It Out (Page 19-21)
Q1. Can you find the angles in the given pictures? Draw the rays forming any one of the angles and name the vertex of the angle — Answer: Yes, angles can be found in the pictures wherever two edges or arms meet at a…
Answer: Yes, angles can be found in the pictures wherever two edges or arms meet at a common point — for example, at the corner of a book, the opened blades of scissors, or the hands of a clock. For any one such angle, draw its two arms as rays starting from the shared corner point; that shared point is the vertex of the angle.
Q2. Draw and label an angle with arms ST and SR — Answer: Draw ray ST and ray SR starting from the same point S. The angle formed between…
Answer: Draw ray ST and ray SR starting from the same point S. The angle formed between them is written as ∠TSR (or ∠RST), with S as the vertex.
Q3. Explain why ∠APC cannot be labelled as ∠P — Answer: The angle cannot be labelled simply as ∠P because three different angles meet…
Answer: The angle cannot be labelled simply as ∠P because three different angles meet at point P in the figure — ∠APC (between rays PA and PC), ∠APB (between rays PA and PB), and ∠BPC (between rays PB and PC). Writing just ∠P would not tell us which of these three angles is meant, so all three letters — A, P and C — must be used, with the vertex letter P written in the middle, to describe the angle unambiguously.
Q4. Name the angles marked in the given figure — Answer: The angles marked in the figure are ∠RTQ and ∠RTP.
Answer: The angles marked in the figure are ∠RTQ and ∠RTP.
Q5. Mark any three points on your paper that are not on one line. Label them A, B, C. Draw all possible lines going through pairs of these points. How many lines do you get? Name them. How many angles can you name using A, B, C? Write them down, and mark each of them with a curve — Answer: Three lines are obtained: line AB, line BC and line CA. Using the three points,…
Answer: Three lines are obtained: line AB, line BC and line CA. Using the three points, three angles can be named: ∠ABC, ∠BCA and ∠CAB. Each of these should be marked with a small curve at its vertex (B, C and A respectively).
Q6. Now, mark any four points on your paper so that no three of them are on one line. Label them A, B, C and D. Draw all possible lines going through pairs of these points. How many lines do you get? Name them. How many angles can you name using A, B, C and D? Write them all down and mark each of them with a curve as in the given figure — Answer: Joining every pair of the four points gives six lines in all: AB, BC, CD, AD, AC…
Answer: Joining every pair of the four points gives six lines in all: AB, BC, CD, AD, AC and BD. Using these points, twelve angles can be named in total: ∠BAC, ∠BAD, ∠CAD, ∠ABD, ∠ABC, ∠DBC, ∠ADB, ∠ADC, ∠BDC, ∠DCA, ∠DCB and ∠ACB. Each of these twelve angles should be marked with a small curve at its vertex.
2.6 Comparing Angles — Figure It Out (Page 23)
Q1. Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the angles formed between the fold and the sides of the paper. Make different angles by folding a rectangular sheet of paper and compare the angles. Which is the largest and smallest angle you made? — Answer: Fold a rectangular sheet at different slants and draw a line along each crease;…
Answer: Fold a rectangular sheet at different slants and draw a line along each crease; each fold creates a pair of angles with the sides of the paper. Comparing the folds made, the angle that opens out the widest (closest to a straight line) is the largest angle, and the angle that is the most “closed up” is the smallest — for example, among the angles ∠1 to ∠5 formed by different folds, ∠5 is the largest and ∠2 is the smallest.
Q2. In each case, determine which angle is greater and why. (a) ∠AOB or ∠XOY (b) ∠AOB or ∠XOB (c) ∠XOB or ∠XOC. Discuss with your friends on how you decided which one is greater — Answer: Comparing the angles by superimposition (placing one angle exactly over the…
Answer: Comparing the angles by superimposition (placing one angle exactly over the other):
- (a) ∠AOB is greater than ∠XOY, since the opening of ∠AOB is wider.
- (b) ∠AOB is greater than ∠XOB, since the opening of ∠AOB is wider.
- (c) ∠XOB and ∠XOC are equal, because they share the vertex O and the common arm OX, and their other arms OB and OC exactly overlap when superimposed.
Q3. Which angle is greater: ∠XOY or ∠AOB? Give reasons — Answer: On comparing the two angles by superimposition, ∠XOY is greater than ∠AOB…
Answer: On comparing the two angles by superimposition, ∠XOY is greater than ∠AOB because its opening (the amount of turn between its arms) is wider than that of ∠AOB.
2.7 Making Rotating Arms, 2.8 Special Types of Angles — Figure It Out (Page 29-31)
Q1. How many right angles do the windows of your classroom contain? Do you see other right angles in your classroom? — Answer: Most classroom windows are rectangular, so each window contains four right…
Answer: Most classroom windows are rectangular, so each window contains four right angles (90° each) at its corners. Other right angles can usually be seen at the corners of the blackboard, the door, desks, books and the walls of the room.
Q2. Join A to other grid points in the figure by a straight line to get a straight angle. What are all the different ways of doing it? — Answer: A straight angle (180°) is formed only when the line through A and the chosen…
Answer: A straight angle (180°) is formed only when the line through A and the chosen grid point continues exactly opposite to an existing arm at A, so that the two arms together form one straight line. On a square grid, this happens for every grid point that lies directly opposite A along a straight row, column or diagonal through A — each such point gives one valid way of forming a straight angle at A.
Q3. Now join A to other grid points in the figure by a straight line to get a right angle. What are all the different ways of doing it? — Answer: First, extend the existing arm at A beyond A to obtain a straight angle; then,…
Answer: First, extend the existing arm at A beyond A to obtain a straight angle; then, through A, draw a line perpendicular to this straight line. On the grid, there is only one grid point that gives a line exactly perpendicular to the base line at A — so there is only one way of forming a right angle at A using the grid points shown.
Q4. Get a slanting crease on the paper. Now, try to get another crease that is perpendicular to the slanting crease. (a) How many right angles do you have now? Justify why the angles are exact right angles. (b) Describe how you folded the paper so that any other person who doesn't know the process can simply follow your description to get the right angle — Answer:
Answer:
- (a) Four right angles are formed at the point where the two creases cross, because folding one straight crease exactly onto itself (the second fold) makes the two halves coincide perfectly, which guarantees that all four angles formed are equal — and since they add up to 360° around the point, each one must be exactly 90°.
- (b) Steps to describe to someone else: First, fold the rectangular sheet slantwise, bringing one corner close to an adjacent edge, and press to create a diagonal (slanting) crease; then unfold. Next, fold the paper again so that the slanting crease falls exactly on top of itself (the two parts of the crease line match up); press along this new fold to create the second crease, then unfold. The point where the two creases cross now has four right angles.
2.7 Making Rotating Arms, 2.8 Special Types of Angles — Figure It Out (Page 31-32)
Q1. Identify acute, right, obtuse and straight angles in the previous figures — Answer: Going back through the earlier rotating-arm and grid figures: angles smaller…
Answer: Going back through the earlier rotating-arm and grid figures: angles smaller than a right angle are acute angles, angles exactly matching the square-corner opening are right angles, angles wider than a right angle but less than a straight line are obtuse angles, and angles that open out into a straight line are straight angles. Each angle in the earlier figures can be sorted into one of these four categories by comparing it with a right-angle corner (such as the corner of a sheet of paper).
Q2. Make a few acute angles and a few obtuse angles. Draw them in different orientations — Answer: Draw several angles with openings smaller than a right angle (acute angles) and…
Answer: Draw several angles with openings smaller than a right angle (acute angles) and several with openings wider than a right angle but less than a straight line (obtuse angles), turning the arms in different directions each time — for example, opening upward, downward, sideways and diagonally — so that the angles are shown in a variety of orientations, not just one fixed position.
Q3. Do you know what the words acute and obtuse mean? Acute means sharp and obtuse means blunt. Why do you think these words have been chosen? — Answer: The word "acute" means "sharp", and an acute angle has a vertex that looks sharp…
Answer: The word “acute” means “sharp”, and an acute angle has a vertex that looks sharp and pointed, like the tip of a needle. The word “obtuse” means “blunt”, and an obtuse angle has a vertex that looks wide and blunt, since its arms are opened out further apart. The names describe how sharp or blunt the angle’s corner appears.
Q4. Find out the number of acute angles in each of the figures below. What will be the next figure and how many acute angles will it have? Do you notice any pattern in the numbers? — Answer: The number of acute angles in the successive star-shaped figures is 3, then 12,…
Answer: The number of acute angles in the successive star-shaped figures is 3, then 12, then 21. In each step, the count increases by 9 (3 + 9 = 12, and 12 + 9 = 21). Following the same pattern, the next figure would have 21 + 9 = 30 acute angles.
2.9 Measuring Angles — Figure It Out (Page 35)
Q1. Write the measures of the following angles: (a) ∠KAL (b) ∠WAL (c) ∠TAK — Answer:
Answer:
- (a) ∠KAL = 30°. Since the vertex of the angle coincides with the centre of the protractor, the number of 1° units between arm AK and arm AL gives the measure directly; counting the marks gives 30°.
- Using the medium and long marks on the protractor, it is also possible to count the units in steps of 5° or 10°, since the scale carries separate markings for every 5° and 10°.
- (b) ∠WAL = 50°. Arms AL and AW pass through markings that are five 10° divisions apart, so ∠WAL = 5 × 10° = 50°.
- (c) ∠TAK = 120°. Arms AK and AT pass through markings that are twelve 10° divisions apart, so ∠TAK = 12 × 10° = 120°.
2.9 Measuring Angles — Figure It Out (Page 40-43)
Q1. Find the degree measures of the following angles using your protractor — Answer: Using the protractor on the three given angles: (a) ∠IHJ = 47°, (b) ∠IHJ =…
Answer: Using the protractor on the three given angles: (a) ∠IHJ = 47°, (b) ∠IHJ = 24°, (c) ∠IHJ = 110°.
Q2. Find the degree measures of different angles in your classroom using your protractor — Answer: Most corners in a classroom — such as the corners of the blackboard, the desk…
Answer: Most corners in a classroom — such as the corners of the blackboard, the desk or the door frame — measure 90° (right angles), since these objects are built with square corners. Other angles, such as the angle at which a partly opened door stands, or the angle of an open book, will vary and should be measured directly with a protractor.
Q3. Find the degree measures for the angles given below. Check if your paper protractor can be used here! — Answer: (a) ∠IHJ = 42°, (b) ∠IHJ = 116°. A simple paper (semicircular) protractor…
Answer: (a) ∠IHJ = 42°, (b) ∠IHJ = 116°. A simple paper (semicircular) protractor cannot be used for every angle shown here, since some of the angles given are reflex angles (greater than 180°), which a semicircular scale cannot measure directly.
Q4. How can you find the degree measure of the angle given below using a protractor? — Answer: The angle shown is a reflex angle, so it cannot be read off a semicircular…
Answer: The angle shown is a reflex angle, so it cannot be read off a semicircular protractor directly. Step 1: Measure the ordinary (non-reflex) angle ∠AOB with the protractor. Step 2: Subtract this measure from 360°, i.e., reflex ∠AOB = 360° − ∠AOB. This gives the required reflex angle.
Q5. Measure and write the degree measures for each of the following angles — Answer:
Answer:
- (a) 80°
- (b) 120°
- (c) 60°
- (d) 130°
- (e) 130°
- (f) 60°
Q6. Find the degree measures of ∠BXE, ∠CXE, ∠AXB and ∠BXC — Answer:
Answer:
- ∠BXE = 115°
- ∠CXE = 85°
- ∠AXB = 180° − ∠BXE = 180° − 115° = 65° (since A, X and E lie on a straight line, AB and BE are supplementary about X)
- ∠BXC = ∠BXE − ∠CXE = 115° − 85° = 30°
Q7. Find the degree measures of ∠PQR, ∠PQS and ∠PQT — Answer: ∠PQR = 45°, ∠PQS = 105°, ∠PQT = 150°.
Answer: ∠PQR = 45°, ∠PQS = 105°, ∠PQT = 150°.
Q8. Make the paper craft as per the given instructions. Then, unfold and open the paper fully. Draw lines on the creases made and measure the angles formed — Answer: This is a hands-on paper-folding activity. Fold the paper as instructed to make…
Answer: This is a hands-on paper-folding activity. Fold the paper as instructed to make the craft, then unfold it completely and trace over each crease with a pencil to turn the creases into visible line segments. Using a protractor, measure the angle formed at each point where creases meet, and record the measures next to each angle — the creases typically produce a mix of acute, right and obtuse angles depending on how the folds were made.
Q9. Measure all three angles of the triangle shown in Fig. (a), and write the measures down near the respective angles. Now add up the three measures. What do you get? Do the same for the triangles in Fig. (b) and (c). Try it for other triangles as well, and then make a conjecture for what happens in general! We will come back to why this happens in a later year — Answer: On measuring the three angles of each triangle and adding them together, the sum…
Answer: On measuring the three angles of each triangle and adding them together, the sum comes out to be 180° every time — this holds for the triangles in Fig. (a), (b) and (c), as well as for any other triangle that is measured. So the conjecture is: ∠A + ∠B + ∠C = 180° for every triangle, i.e., the sum of the three angles of a triangle is always 180°.
2.9 Measuring Angles — Figure It Out (Page 45-46)
Q1. Angles in a clock: (a) The hands of a clock make different angles at different times. At 1 O'clock, the angle between the hands is 30°. Why? (b) What will be the angle at 2 O'clock? And at 4 O'clock? 6 O'clock? (c) Explore other angles made by the hands of a clock — Answer:
Answer:
- (a) A clock face is divided into 12 equal hour marks around a full circle of 360°, so each hour mark is 360° ÷ 12 = 30° apart. At 1 O’clock, the hour hand is at the 1-mark and the minute hand is at the 12-mark, exactly one hour-mark apart, so the angle between them is 30°.
- (b) At 2 O’clock, the angle is 2 × 30° = 60°. At 4 O’clock, the angle is 4 × 30° = 120°. At 6 O’clock, the angle is 6 × 30° = 180° (a straight angle).
- (c) In general, at n O’clock (for n from 1 to 6), the angle between the hands is n × 30°; for example, the angle is 90° at 3 O’clock and 150° at 5 O’clock. Beyond 6 O’clock, the smaller angle between the hands is found by measuring the shorter way around, i.e., 360° minus n × 30°.
Q2. The angle of a door. Is it possible to express the amount by which a door is opened using an angle? What will be the vertex of the angle and what will be the arms of the angle? — Answer: Yes, the amount by which a door is opened can be expressed as an angle. The…
Answer: Yes, the amount by which a door is opened can be expressed as an angle. The hinge of the door is the vertex of the angle, and the two arms of the angle are the wall (or door frame) and the edge of the door itself — the wider the door swings open, the larger this angle becomes.
Q3. Vidya is enjoying her time on the swing. She notices that the greater the angle with which she starts the swinging, the greater is the speed she achieves on her swing. But where is the angle? Are you able to see any angle? — Answer: Yes, an angle can be seen here. The vertex of the angle is the point where the…
Answer: Yes, an angle can be seen here. The vertex of the angle is the point where the swing’s rope is tied (the top support). One arm of the angle is the vertical line straight down from that point (the position of the rope when the swing is at rest), and the other arm is the rope in its slanted, pulled-back starting position — the angle between them is the “starting angle” of the swing.
Q4. Here is a toy with slanting slabs attached to its sides; the greater the angles or slopes of the slabs, the faster the balls roll. Can angles be used to describe the slopes of the slabs? — Answer: Yes, angles can describe the slope of each slab. For each slab, one arm of the…
Answer: Yes, angles can describe the slope of each slab. For each slab, one arm of the angle is the horizontal base (or a horizontal line parallel to it) and the other arm is the slanting slab itself. The greater this angle, the steeper the slope, and the faster the ball rolls down.
Q5. Observe the images below where there is an insect and its rotated version. Can angles be used to describe the amount of rotation? How? What will be the arms of the angle and the vertex? (Hint: Observe the horizontal line touching the insects.) — Answer: Yes, angles can describe the amount of rotation. The vertex of the angle is the…
Answer: Yes, angles can describe the amount of rotation. The vertex of the angle is the point about which the insect turns, one arm is the insect’s original (initial) position relative to the horizontal reference line, and the other arm is its final, rotated position — the angle between the two arms gives the amount of rotation. In the given images, both insects have been rotated by 90° (a quarter turn) in the clockwise direction.
2.10 Drawing Angles — Figure It Out (Page 49-50)
Q1. In the given figure below, list all the angles possible. Did you find them all? Now, guess the measures of all the angles. Then, measure the angles with a protractor. Record all your numbers in a table. See how close your guesses are to the actual measures — Answer: A sample recording table, comparing estimated and actual (protractor-measured)…
Answer: A sample recording table, comparing estimated and actual (protractor-measured) values:
- ∠PAC — estimated 100°, actual 107°
- ∠ACD — estimated 80°, actual 72°
- ∠CDL — estimated 180°, actual 180°
- ∠DLP — estimated 95°, actual 97°
- ∠LPR — estimated 95°, actual 98°
- ∠PLS — estimated 85°, actual 82°
- ∠LSR — estimated 75°, actual 78°
- ∠PRS — estimated 105°, actual 102°
- ∠BRS — estimated 75°, actual 79°
Estimates made by eye are usually close to, but not exactly equal to, the values measured with a protractor — this activity shows how good your angle-estimation skills are and encourages checking every estimate with an actual measurement.
Q2. Use a protractor to draw angles having the following degree measures: (a) 110° (b) 40° (c) 75° (d) 112° (e) 134° — Answer: For each angle, follow these steps: Step 1 — draw a ray, say AB. Step 2 –…
Answer: For each angle, follow these steps: Step 1 — draw a ray, say AB. Step 2 — place the centre of the protractor exactly at A, with its base line along AB. Step 3 — starting the count from 0° at B, mark a point at the required degree measure (110°, 40°, 75°, 112° or 134° respectively). Step 4 — join A to this marked point, say P; the angle ∠BAP formed is the required angle. Repeating this process for each of the five given measures gives all five required angles.
Q3. Draw an angle whose degree measure is the same as the angle given below. Also, write down the steps you followed to draw the angle — Answer: Step 1 — measure the given angle with a protractor (here, ∠IHJ = 120°). Step…
Answer: Step 1 — measure the given angle with a protractor (here, ∠IHJ = 120°). Step 2 — using a protractor, draw a fresh angle of the same measure, for example ∠ABC = 120°, following the usual ray-and-protractor method (draw ray AB, place the protractor centre at A, mark the point at 120° from B, and join it to A).
2.11 Types of Angles and their Measures — Figure It Out (Page 51-52)
Q1. In each of the below grids, join A to other grid points in the figure by a straight line to get (a) an acute angle (b) an obtuse angle (c) a reflex angle. Mark the intended angles with curves to specify the angles. One has been done for you — Answer:
Answer:
- (a) Join A to a grid point so that the new arm makes an opening of less than 90° with the existing arm at A — this gives an acute angle; mark it with a small curve.
- (b) Join A to a grid point so that the new arm makes an opening of more than 90° but less than 180° with the existing arm at A — this gives an obtuse angle; mark it with a curve.
- (c) Join A to a grid point so that the angle measured the “long way round” (on the outside of the figure) is more than 180° but less than 360° — this gives a reflex angle; mark this larger opening with a curve.
Q2. Use a protractor to find the measure of each angle. Then classify each angle as acute, obtuse, right, or reflex. (a) ∠PTR (b) ∠PTQ (c) ∠PTW (d) ∠WTP — Answer:
Answer:
- (a) ∠PTR = 31°, an acute angle (less than 90°)
- (b) ∠PTQ = 60°, an acute angle (less than 90°)
- (c) ∠PTW = 104°, an obtuse angle (between 90° and 180°)
- (d) ∠WTP = 360° − 104° = 256°, a reflex angle (between 180° and 360°)
2.11 Types of Angles and their Measures — Figure It Out (Page 53-54)
Q1. Draw angles with the following degree measures: (a) 140° (b) 82° (c) 195° (d) 70° (e) 35° — Answer: Using a protractor, draw each angle by the standard method: draw a base ray,…
Answer: Using a protractor, draw each angle by the standard method: draw a base ray, place the protractor’s centre at its starting point, count off the required number of degrees from 0°, mark the point, and join it back to the starting point. This gives five separate angles of measure 140°, 82°, 195° (a reflex angle — drawn by marking 195° − 180° = 15° past the straight-line position, or by measuring 360° − 195° = 165° from the other side), 70° and 35° respectively.
Q2. Estimate the size of each angle and then measure it with a protractor. Classify these angles as acute, right, obtuse or reflex angles — Answer:
Answer:
- (a) 45° — acute angle
- (b) 169° — obtuse angle
- (c) 120° — obtuse angle
- (d) 33° — acute angle
- (e) 99° — obtuse angle
- (f) 348° — reflex angle
Q3. Make any figure with three acute angles, one right angle and two obtuse angles — Answer: Draw any closed figure (for example, an irregular six-sided shape) in which…
Answer: Draw any closed figure (for example, an irregular six-sided shape) in which three of the interior or marked angles measure less than 90° (acute), one angle measures exactly 90° (right), and two angles measure between 90° and 180° (obtuse). Label each angle with its measure to confirm the figure meets all three conditions.
Q4. Draw the letter 'M' such that the angles on the sides are 40° each and the angle in the middle is 60° — Answer: Draw the letter M using four strokes — two outer vertical strokes and two inner…
Answer: Draw the letter M using four strokes — two outer vertical strokes and two inner slanting strokes meeting at the centre. Using a protractor, make the angle between each outer vertical stroke and its adjacent slanting stroke equal to 40°, and make the angle between the two slanting strokes where they meet in the middle equal to 60°.
Q5. Draw the letter 'Y' such that the three angles formed are 150°, 60° and 150° — Answer: Draw the letter Y with its three strokes meeting at a single central point (the…
Answer: Draw the letter Y with its three strokes meeting at a single central point (the two upper arms and the lower stem). Using a protractor, set the angle between one upper arm and the lower stem to 150°, the angle between the two upper arms to 60°, and the angle between the other upper arm and the lower stem to 150° — note that these three angles together make a full turn: 150° + 60° + 150° = 360°.
Q6. The Ashoka Chakra has 24 spokes. What is the degree measure of the angle between two spokes next to each other? What is the largest acute angle formed between two spokes? — Answer: A full circle measures 360°, and the 24 spokes divide it into 24 equal parts,…
Answer: A full circle measures 360°, and the 24 spokes divide it into 24 equal parts, so the angle between two adjacent spokes is 360° ÷ 24 = 15°. Since angles between any two spokes are always whole-number multiples of 15° (15°, 30°, 45°, 60°, 75°, 90°, 105°, …), the largest acute angle (an angle less than 90°) that can be formed between two spokes is 75° — the next multiple, 90°, is a right angle, not acute.
Note: Some other solution sources state the largest acute angle as 15°, but this simply repeats the angle between adjacent spokes and does not answer the question asked. Working through the multiples of 15° up to (but not including) 90° shows that 75° is the correct largest acute angle.
Q7. Puzzle: I am an acute angle. If you double my measure, you get an acute angle. If you triple my measure, you will get an acute angle again. If you quadruple (four times) my measure, you will get an acute angle yet again! But if you multiply my measure by 5, you will get an obtuse angle measure. What are the possibilities for my measure? — Answer: Let the angle be x. The conditions require 4x to still be less than 90°…
Answer: Let the angle be x. The conditions require 4x to still be less than 90° (acute), and 5x to be greater than 90° (obtuse) — so 90°/5 < x < 90°/4, i.e., 18° < x < 22.5°. The whole-number values of x satisfying this are 19°, 20°, 21° and 22°.
Practice more: Extra Questions for Class 6 Maths Chapter 2
Quick revision: Revision Notes for Class 6 Maths Chapter 2
- Chapter 1: Patterns in Mathematics - Ganita Prakash
- Chapter 3: Number Play NCERT Solutions
- Chapter 4: Data Handling and Presentation NCERT Solutions
- Chapter 5: Prime Time NCERT Solutions
- Chapter 6: Perimeter and Area NCERT Solutions
- Chapter 7: Fractions NCERT Solutions
- Chapter 8: Playing with Constructions NCERT Solutions
- Chapter 9: Symmetry – Free PDF Download
- Chapter 10: The Other Side of Zero – Free PDF Download
Frequently Asked Questions
What is the difference between complementary and supplementary angles?
Complementary angles are two angles whose measures add up to 90 degrees; supplementary angles are two angles whose measures add up to 180 degrees — mixing these two definitions up is one of the most common errors in this chapter.
What is the relationship between angles formed when a transversal cuts two parallel lines?
Corresponding angles are equal, alternate interior angles are equal, and co-interior (allied) angles add up to 180 degrees — these three angle relationships are the foundation for solving nearly every parallel-lines problem in this chapter.
Chapter Quiz — Test Your Understanding
Class 6 Mathematics Chapter 2 – Notes and Extra Questions
Along with these NCERT Solutions, students can also use the Class 6 Mathematics Chapter 2 Extra Questions and Class 6 Mathematics Chapter 2 Revision Notes for quick revision and extra practice.
Recommended: Buy the Printed NCERT Class 6 Maths Book
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