Question

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

Answer 1

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

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

Sum of interior angles of a polygon = (n - 2) × 180°

= (5 - 2) × 180°

= 540°

∴ 27x = 540 

⇒ x = `540/27`

⇒ x = 20°

∴ Angles are 4 × 20° = 80°

5 × 20° = 100°

6 × 20° = 120°

7 × 20° = 140°

5 × 20° = 100°