Extra Questions for Class 7 Maths Chapter 7: A Tale of Three Intersecting Lines – HOTS

Fresh HOTS practice questions for Class 7 Maths Chapter 7 “A Tale of Three Intersecting Lines”, testing the triangle inequality, angle sum property, and exterior angle theorem with new numbers. These Class 7 Mathematics Chapter 7 important questions are handy for last-minute exam practice.

Last Updated: September 23, 2026

Q1. Can a triangle have side lengths 6 cm, 7 cm, and 14 cm? Justify your answer.

Answer: No. Since 6+7 = 13, which is less than 14, the triangle inequality fails, so this triangle cannot exist.

Q2. Two sides of a triangle are 9 cm and 4 cm. What is the range of possible values for the third side?

Answer: The third side must satisfy (9−4) < third side < (9+4), i.e., strictly between 5 cm and 13 cm.

Q3. Assertion-Reason — Assertion (A): A triangle with angles 100°, 50°, 40° is valid. Reason (R): The three…

Assertion (A): A triangle with angles 100°, 50°, 40° is valid.
Reason (R): The three angles must sum to 180°.

Answer: R is true, but A is false (100+50+40 = 190° ≠ 180°), so this angle set is invalid. Since A is false, the combined statement is incorrect.

Q4. In a triangle, one angle is 90° and another is 35°. Find the third angle and classify the triangle by its angles.

Answer: Third angle = 180 − 90 − 35 = 55°. Since one angle is exactly 90°, this is a right-angled triangle.

Q5. Spot the error — A student says: "Since 4+5=9 and the third side is 9, a triangle with sides 4, 5, 9 is…

A student says: “Since 4+5=9 and the third side is 9, a triangle with sides 4, 5, 9 is valid.” Identify and correct the error.

Answer: This is incorrect. The triangle inequality requires the sum of two sides to be strictly greater than the third side, not equal to it. Since 4+5=9 exactly equals the third side, the triangle is degenerate (the three points would be collinear) and does not form a valid triangle.

Q6. The exterior angle of a triangle at vertex C is 130°, and one of the remote interior angles (at A) is 55°. Find the interior angle at B.

Answer: By the Exterior Angle Theorem, exterior angle = sum of remote interior angles: 130 = 55 + angle B, so angle B = 75°.

Q7. Can an isosceles triangle have angles 50°, 50°, and 80°? Verify and classify the triangle.

Answer: Yes. The angles sum to 50+50+80=180° ✓, and two angles are equal (50° each), confirming it is isosceles. Since all angles are less than 90°, it is also an acute-angled triangle.

Q8. A triangle has sides 8 cm, 8 cm, and 8 cm. Classify this triangle by both its sides and its angles.

Answer: By sides: equilateral (all three sides equal). By angles: each angle = 180÷3 = 60°, so it is also acute-angled (specifically, equiangular).

Q9. Two angles of a triangle are 48° and 48°. What type of triangle is this (by sides)?

Answer: Since two angles are equal, the sides opposite them are also equal, making this an isosceles triangle. Third angle = 180−48−48 = 84°.

Q10. Explain why a triangle can never have two obtuse angles.

Answer: If a triangle had two angles each greater than 90°, their sum alone would already exceed 180°, leaving no room for a positive third angle. Since all three angles must sum to exactly 180°, at most one angle can be obtuse (or right).

NCERT Solutions: Class 7 Maths Chapter 7

Revision Notes: Class 7 Maths Chapter 7 Revision Notes

Frequently Asked Questions

If two angles of a triangle measure 50 degrees and 60 degrees, what is the measure of the third angle?
Since the three interior angles of any triangle always add up to 180 degrees, the third angle is found by subtracting the sum of the two known angles, 110 degrees, from 180 degrees, giving 70 degrees.

How can the exterior angle property help find an unknown angle without calculating every interior angle of a triangle?
Since an exterior angle equals the sum of the two interior opposite angles, if those two angles are known, the exterior angle can be found directly by adding them.

Written by Satish

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