Question

The angles of a pentagon are x°, (x - 10)°, (x + 20)°, (2x - 44)° and (2x - 70)°. Find the angles.

Answer 1

A pentagon has 5 sides
∴ Sum of interior angles
= (n - 2) x 180°
= (5 - 2) x 180°
= 3 x 180°
= 540°
Given, the angles are x°, (x - 10)°, (x + 20)°, (2x - 44)° and (2x - 70)°
∴ x °+ (x - 10)° + (x + 20)° + (2x - 44)° + (2x - 70)° = 540°
⇒ 7x° - 104° = 540°

⇒ x = `((540° + 104°))/(7)` = 92°

∴ The interior angles of the pentagon are 92°, 82°, 112°, 140° and 114°.