Extra Questions for Class 7 Maths Chapter 5: Parallel and Intersecting Lines – HOTS

Fresh HOTS practice questions for Class 7 Maths Chapter 5 “Parallel and Intersecting Lines”, testing angle-relationship concepts with new numbers. These Class 7 Mathematics Chapter 5 important questions are handy for last-minute exam practice.

Q1.

Two parallel lines are cut by a transversal. One of the co-interior angles is 72°. Find the other co-interior angle.

Answer: Co-interior angles sum to 180°, so the other angle = 180° − 72° = 108°

Q2.

If two lines intersect and one of the four angles formed is 35°, find the other three angles.

Answer: The angle vertically opposite 35° is also 35°. The two remaining angles (forming linear pairs with 35°) are each 180° − 35° = 145°. So the four angles are 35°, 145°, 35°, 145°

Q3. Assertion-Reason

Assertion (A): If a transversal crosses two parallel lines, corresponding angles are equal.
Reason (R): Corresponding angles occupy the same relative position at each intersection point.

Answer: Both A and R are true, and R correctly explains A.

Q4.

Two lines l and m are both perpendicular to line n. What is the relationship between l and m, and why?

Answer: Lines l and m are parallel to each other, because two lines that are each perpendicular to the same line must be parallel.

Q5. Spot the error

A student claims: “Since angle 1 and angle 2 are vertically opposite angles, they add up to 180°.” Identify and correct the error.

Answer: This is incorrect. Vertically opposite angles are always equal to each other, not supplementary. It is linear pairs (adjacent angles on a straight line) that add up to 180°.

Q6.

In a figure, a transversal crosses two parallel lines. One interior angle on one side is 3x, and the co-interior angle on the same side is 2x + 30°. Find x and both angles.

Answer: 3x + (2x+30) = 180 ⇒ 5x + 30 = 180 ⇒ 5x = 150 ⇒ x = 30. Angles: 3(30) = 90° and 2(30)+30 = 90°

Q7.

A ladder leans against a wall such that it makes a 65° angle with the ground. What angle does it make with the wall (assuming the wall is perpendicular to the ground)?

Answer: The ladder, wall, and ground form a right triangle where the ground and wall meet at 90°. The angle with the wall = 90° − 65° = 25°

Q8.

Two parallel railway tracks are crossed by a diagonal road (transversal). If the angle between the road and one track is 58°, what is the angle between the road and the other track on the same side (co-interior)?

Answer: 180° − 58° = 122°

Q9.

Explain, with reasoning, whether two lines that are both parallel to a third line must be parallel to each other.

Answer: Yes. If line A is parallel to line C, and line B is parallel to line C, then line A must be parallel to line B, since both maintain a constant, non-intersecting distance from line C in the same plane, and cannot converge with each other either.

Q10.

In a figure, alternate interior angles are marked (5x − 10)° and (3x + 20)°. Find x and the measure of each angle.

Answer: Alternate interior angles are equal: 5x−10 = 3x+20 ⇒ 2x = 30 ⇒ x = 15. Each angle = 5(15)−10 = 65°

NCERT Solutions: Class 7 Maths Chapter 5

Revision Notes: Class 7 Maths Chapter 5 Revision Notes

Written by Satish

NCERTBooks.org is an independent educational resource run by a small team focused on making official NCERT textbooks easy to find, read, and download for students, parents, and teachers across India. We are not affiliated with NCERT or the Ministry of Education -- we organise publicly available NCERT content by class and subject, verify links against official sources, and build tools (like our in-browser reader) that make studying more convenient. Every guide we publish is written and reviewed by our team based on the actual NCERT curriculum and syllabus.