# EXERCISE – 6.2

Q1. Find the value of the unknown exterior angle x in the following diagrams:

SOLUTION:-

(i) We know that.

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

= x = 500 + 700

= x = 1200

(ii) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles

= x = 650 + 450

= x = 1100

(iii) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

= x = 300 +

400

= x = 700

(iv) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

= x = 600 + 600

= x = 1200

(v) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

= x = 500 + 500

= x = 1000

(vi) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

= x = 300 + 600

= x = 900

Q2. Find the value of the unknown interior angle x in the following figures

SOLUTION:-

(i) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angle

= x + 500 = 1150

= x = 1150 – 500

= x = 650

(ii) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

=  700 + x = 1000

= x = 1000 – 700

= x = 300

(iii) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

The given triangle is a right angled triangle. So the angle opposite  to the x is 900

= x + 900 = 1250

= x = 1250 – 900

= x = 350.

(iv) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

= x + 600 = 1200

= x = 1200 – 600

= x = 600.

(v) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles

= x + 300 = 800

= x = 800 – 300

= x = 500

(vi) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles

= x + 350 = 750

= x = 750 – 350

= x = 400