Question

The angles of a pentagon are in the ratio 5 : 4 : 5 : 7 : 6 ; find each angle of the pentagon.

Answer 1

Let the angles of the pentagon be 5x, 4x, 5x, 7x, 6x

Their sum = 5x + 4x + 5x + 7x + 6x = 27x

Sum of interior angles of a polygon

= (2n - 4) × 90°

= (2 × 5 - 4) × 90° = 540°

∴ 27x = 540 ⇒ `540/27`

⇒ x = 20°

∴ Angles are 5 × 20° = 100°

4 × 20° = 80°

5 × 20° = 100°

7 × 20° = 140°

6 × 20° = 120°