Question

One angle of a pentagon is 160° and the rest are all equal angles. Find the measure of the equal angles.

Answer 1

A pentagon has 5 sides
∴ Sum of interior angles
= (n - 2) x 180°
= (5 - 2) x 180°
= 3 x 180°
= 540°
One angle is given to be 160°
Ratio of the remaining four angles
= 1 : 1 : 1 : 1
∴ The interior angles are x°, x°, x° and x°
∴ 160° + x° + x° + x° + x° = 540°
⇒ 4x° = 540° - 160° = 380°
⇒ x° = 95°
∴ Each equal angle is 95°.