Question

Find the angles of a quadrilateral whose angles are in the ratio 1: 4: 5: 2.

Answer 1

A quadrilateral is a polygon with four sides
∴ Sum of interior angles
= (n - 2) x 180°
= (4 - 2) x 180°
= 2 x 180°
= 360°
Ratio of the angles 
= 1: 4: 5: 2
∴  The interior angles are x°, 4x°, 5x° and 2x°.
∴ x + 4x° + 5x° + 2x° = 360°
⇒ 12x° = 360°
⇒ x° = 30°
∴ The interior angles of the quadrilateral are 30°, 120°, 150° and 60°.