The angles of a pentagon are in the ratio 4 : 8 : 6 : 4 : 5. Find each angle of the pentagon.

By formula,

Sum of interior angles of an 'n' sided polygon = (2n - 4) × 90°.

Sum of interior angles of a pentagon = [2 × 5 - 4] × 90°

= [10 - 4] × 90°

= 6 × 90°

= 540°.

Given,

The angles of a pentagon are in the ratio 4 : 8 : 6 : 4 : 5.

Let angles be 4x, 8x, 6x, 4x and 5x.

⇒ 4x + 8x + 6x + 4x + 5x = 540°

⇒ 27x = 540°

⇒ x = $\dfrac{540°}{27}$ = 20°.

⇒ 4x = 4(20°) = 80°, 8x = 8(20°) = 160°, 6x = 6(20°) = 120°, 4x = 4(20°) = 80° and 5x = 5(20°) = 100°.

Hence, angles of pentagon are 80°, 160°, 120°, 80° and 100°.