**NCERT Solutions for Class 7 Maths**

Chapter 6 The Triangle and its Properties

Exercise 6.2

Chapter 6 The Triangle and its Properties

Exercise 6.2

**1. Find the value of the unknown exterior angle x in the following diagrams:**

**Answer**

By exterior angle property of a triangle,

Exterior angle = Sum of interior opposite angles

⇒ x=50°+ 70° = 120°

Hence, the exterior angle x is 120°.

(ii) By exterior angle property of a triangle,

Exterior angle = Sum of interior opposite angles

⇒ x= 65°+ 45°= 110°

Hence, the exterior angle x is 110°.

(iii) By exterior angle property of a triangle,

Exterior angle = Sum of interior opposite angles

⇒ x=30° + 40°= 70°

Hence, the exterior angle x is 70°.

(iv) By exterior angle property of a triangle,

Exterior angle = Sum of interior opposite angles

⇒ x= 60° + 60° = 120°

Hence, the exterior angle x is 120°.

(v) By exterior angle property of a triangle,

Exterior angle = Sum of interior opposite angles

∴ x = 50° +50° = 100°

Hence, the exterior angle x is 100°.

(vi) By exterior angle property of a triangle,

Exterior angle = Sum of interior opposite angles

⇒ x = 30°+ 60° = 90°

Hence, the exterior angle x is 90°.

**2. Find the value of the unknown interior angle x in the following figures:**

**Answer**

⇒ x = 115° – 50° = 65°

Hence, the value of the unknown interior angle x is 65°.(ii) Sum of interior opposite angles = Exterior angle

⇒ x+ 70° =100°

⇒ x = 100° – 70° = 30°

Hence, the value of the unknown interior angle x is 30°.

(iii) Sum of interior opposite angles = Exterior angle

⇒ x+90° = 125°

⇒ x = 125° – 90°= 35°

Hence, the value of the unknown interior angle x is 35°.

(iv) Sum of interior opposite angles = Exterior angle

⇒ x+60° =120°

⇒ x=120° – 60° = 60°

Hence, the value of the unknown interior angle x is 60°.

(v) Sum of interior opposite angles = Exterior angle

⇒ x+ 30° = 80°

⇒ x= 80° – 30° = 50°

Hence, the value of the unknown interior angle x is 50°.

(vi) Sum of interior opposite angles = Exterior angle

⇒ x+35° = 75°

⇒ x = 75°- 35° = 40°

Hence, the value of the unknown interior angle x is 40°.