Question

5. The angles of a pentagon are in the ratio 4:5:11:13:12. Find the measures of each angle.

Answer 1

Answer:

Measure of each angle is 48°,60°,132°,156° and 144°

Step-by-step explanation:

Given the pentagon have 5 angles

∴ All angles measure up to 540°

∵Angles of a pentagon are in the ratio 4:5:11:13:12

Let x be the common multiple, then we have

4x+5x+11x+13x+12x = 540

→ 45x = 540

∴ x = 12

∴ 4x= 4x12 =48°

5x = 5x12 = 60°

11x = 11x12 = 132°

13x = 13x12 = 156°

12x = 12x12 = 144°

thus measure of each angle is 48°,60°,132°,156° and 144°