These NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.3 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Exercise 6.3

Question 1.

Find the value of the unknown x in the following diagrams:

Answer:

(i) x + 50° + 60°= 180°

(angle sum property of a triangle)

x + 110° = 180°

x = 180°- 110°

= 70°

∠x = 70°

(ii) x + 90° + 30°= 180°

(angle sum property of a triangle)

x + 120° = 180°

x = 180° – 120°

= 60°

∠x = 60°

(iii) 30° + 110° + x = 180°

(angle sum property of a triangle)

140°+ x = 180°

x = 180° – 140°

= 40°

∠x =40°

(iv) x + x + 50°= 180°

(angle sum property of a triangle)

2x + 50° = 180°

2x = 180° – 50°

2x = 130°

x = \(\frac{130^{\circ}}{2}\) = 65°

∠x = 65°

(v) x + x + x = 180°

(angle sum property of a triangle)

3x = 180°

x = \(\frac{180^{\circ}}{3}\)

x = 60°

∠x = 60°

(vi) x + 2x + 90° = 180°

(angle sum property of a triangle)

3x + 90° = 180°

3x = 180° – 90°

= 90°

x = \(\frac{90^{\circ}}{3}\)

= 30°

∴ ∠x = 30°

Question 2.

Find the values of the unknown x and y in the following diagrams:

Answer:

(i) ∠y + 120°= 180°

(linear pair of angles)

∠y = 180° – 120°

= 60°

∠x + ∠y + 50° = 180°

(using the angle sum property of a triangle)

∠x + 60° + 50° = 180°

∠x + 110° = 180°

∠x = 180°- 110°

= 70°

Thus, ∠x = 70° and ∠y = 60°

(ii) ∠y = 80°

(vertically opposite angles are equal)

∠x + ∠y + ∠50° = 180°

(using the angle sum property of a triangle)

∠x + 80° + 50°= 180°

∠x + 130° = 180°

∠x = 180° – 130°

= 50°

Thus, ∠x = 50° and ∠y = 80°

(iii) 50° + 60° + ∠y = 180°

(using the angle sum property of a triangle)

110° + ∠y – 180°

∠y = 180°- 110°

= 70°

∠x and ∠y form a linear pair.

∠x + ∠y = 180°

∠x + 70° = 180°

∠x = 180° – 70°

= 110°

Thus, ∠x =110° and ∠y = 70°

(iv) ∠x = 60°

(vertically opposite angles)

∠x+ ∠y + 30° = 180°

(angle sum property of a triangle)

60° + ∠y + 30° = 180°

∠y + 90° = 180°

∠y = 180° – 90°

∠y = 90°

Thus, ∠x = 60° and ∠y = 90°

(v) ∠y = 90°

(vertically opposite angles are equal)

∠x + ∠x + ∠y = 180°

(angle sum property of triangle)

2∠x + 90° = 180°

2x = 180° – 90°

2x = 90°

x = \(\frac{90^{\circ}}{2}\) = 45°

Thus, ∠y = 90°,∠x = 45°

(vi) One angle of the triangle = y

Each of the other two angles is equal to their vertically opposite angle ‘x’

∠x + ∠x + ∠y = 180°

(angle sum property of a triangle)

2x + y = 180°

2x + x = 180°

3x = 180°

x = \(\frac{180^{\circ}}{3}\)

x = 60°

y = x

(Vertically opposite angles) y = 60°

Thus, x = 60° and y = 60°