# Find the angle measure x in the following figures:

**Solution:**

(a) The given figure has 4 sides and hence it is a quadrilateral

Using the angle sum property of a quadrilateral,

50° + 130° + 120° + x = 360°

300° + x = 360°

x = 360° - 300°

x = 60°

(b) Using the angle sum property of a quadrilateral.

The line is perpendicular to the base line hence, the angle formed is 90°.

90° + 60° + 70° + x = 360°

220° + x = 360°

220° + x = 360°

x = 360° - 220°

x = 140°

(c) The given figure is a pentagon (number of sides =5)

Angle sum of a polygon = (n - 2) × 180°

= (5 - 2) × 180°

= 3 × 180°

= 540°

Sum of the interior angle of pentagon is 540°.

Angles at the bottom are linear pairs.

Thus, First base interior angle,

= 180° - 70° (angle of straight line is 180° )

= 110°

Also, Second base interior angle,

= 180° - 60°

= 120°

Angle sum property of a polygon = (n - 2) × 180°

⇒ 30° + x + 110° + 120° + x = 540°

⇒ 2x + 260° = 540°

⇒ 2x = 540° - 260°

⇒ 2x = 280°

⇒ x = 280°/2

Therefore, x = 140°

(d) The given figure is pentagon (number of sides =5)

Sum of the interior angle of pentagon is 540°

Angle sum of a polygon

= (n - 2) × 180°

= (5 - 2) × 180°

= 3 × 180°

= 540°

Let each angle of the polygon be x since it is a regular pentagon.

Angle sum of a polygon = x + x + x + x + x = 540°

5x = 540°

x = 540°/5

x = 108°

The given pentagon is a regular polygon i.e. it is both ‘equilateral’ and ‘equiangular’. Thus, the measure of each interior angle of the pentagon is equal.

Hence each interior angle is 108°

**Video Solution:**

## Find the angle measure x in the following figures:

### NCERT Solutions Class 8 Maths - Chapter 3 Exercise 3.1 Question 6

**Summary:**

The angle measure of x in the following figures are: (a) 60° (b) 140° (c) 140° (d) 108°.