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

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:

(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:

(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°

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