A Tale of Three Intersecting Lines — Class 7 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 7 Mathematics chapter "A Tale of Three Intersecting Lines" — 8 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "A Tale of Three Intersecting Lines" — 8 important questions with detailed answers f…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

Define a triangle and state the sum of its interior angles.
In a triangle, two angles are 50° and 70°. Find the third angle.
What is an exterior angle of a triangle? State the exterior angle theorem.
The exterior angle of a triangle is 110°. If one of the remote interior angle…
Classify triangles based on sides and angles.
In triangle ABC, angle A = 35°, angle B = 65°. Classify the triangle by angle…
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
Define a triangle and state the sum of its interior angles.	✓ Solved
In a triangle, two angles are 50° and 70°. Find the third…	✓ Solved
What is an exterior angle of a triangle? State the exteri…	✓ Solved
The exterior angle of a triangle is 110°. If one of the r…	✓ Solved
Classify triangles based on sides and angles.	✓ Solved
In triangle ABC, angle A = 35°, angle B = 65°. Classify t…	✓ Solved

Showing 6 of 8 questions

Q1: Define a triangle and state the sum of its interior angles.

Step 1: Definition of a triangle: A triangle is a closed figure formed by three line segments (sides) connecting three non-collinear points (vertices). Step 2: Parts of a triangle: - Three sides (line segments) - Three vertices (corners/angles) - Three interior angles Step 3: Angle sum property of a triangle: The sum of all interior angles of a triangle is always 180°. If the angles are A, B, and C, then: A + B + C = 180° Answer: A triangle is a closed figure with three sides and three vertic...

Q2: In a triangle, two angles are 50° and 70°. Find the third angle.

Step 1: Use the angle sum property of a triangle: Angle 1 + Angle 2 + Angle 3 = 180° Step 2: Substitute known values: 50° + 70° + Angle 3 = 180° 120° + Angle 3 = 180° Step 3: Solve for Angle 3: Angle 3 = 180° - 120° = 60° Step 4: Verify: 50° + 70° + 60° = 180° ✓ Answer: The third angle is 60°.

Q3: What is an exterior angle of a triangle? State the exterior angle theorem.

Step 1: Definition of exterior angle: An exterior angle of a triangle is formed when one side of the triangle is extended beyond a vertex. Step 2: Exterior angle theorem: An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles (also called remote interior angles). Step 3: Example: In triangle ABC, if side BC is extended to point D, the exterior angle ACD equals angle A + angle B. Angle ACD = Angle A + Angle B Step 4: Relationship to angle sum: Exterior angl...

Q4: The exterior angle of a triangle is 110°. If one of the remote interior angles is 60°, find the other remote interior angle.

Step 1: Apply the exterior angle theorem: Exterior angle = Remote interior angle 1 + Remote interior angle 2 Step 2: Substitute known values: 110° = 60° + Remote interior angle 2 Step 3: Solve: Remote interior angle 2 = 110° - 60° = 50° Step 4: Verify: Sum of remote angles = 60° + 50° = 110° = Exterior angle ✓ Answer: The other remote interior angle is 50°.

Q5: Classify triangles based on sides and angles.

Step 1: Classification based on SIDES: (a) Equilateral triangle: All three sides are equal All angles = 60° each (b) Isosceles triangle: Two sides are equal The angles opposite the equal sides are equal (c) Scalene triangle: All three sides are unequal All angles are unequal Step 2: Classification based on ANGLES: (a) Acute triangle: All three angles are less than 90° All angles are acute (b) Right triangle (Right-angled): One angle is exactly 90° The other two angles a...

Q6: In triangle ABC, angle A = 35°, angle B = 65°. Classify the triangle by angles. Also find the exterior angle at C.

Step 1: Find angle C using angle sum property: Angle A + Angle B + Angle C = 180° 35° + 65° + Angle C = 180° 100° + Angle C = 180° Angle C = 80° Step 2: Classify by angles: All angles (35°, 65°, 80°) are less than 90°. Therefore, this is an ACUTE triangle. Step 3: Find exterior angle at C: Exterior angle at C = Angle A + Angle B (by exterior angle theorem) Exterior angle at C = 35° + 65° = 100° Step 4: Verify: Exterior angle + Interior angle C = 100° + 80° = 180° ✓ (linear pair) Answer: The ...

Showing 6 of 8 questions. Visit the full page for complete solutions.