The angles of a quadrilateral are in A.P. If the greatest angle is double of the smallest angle, find all the four angles.

Let the angles of quadrilateral be a, (a + d), (a + 2d), (a + 3d).

According to question greatest angle is twice the smallest angle,

⇒ (a + 3d) = 2a
⇒ 2a - a = 3d
⇒ a = 3d.

By putting values of a = 3d , the angles become,

a = 3d

a + d = 3d + d = 4d

a + 2d = 3d + 2d = 5d

a + 3d = 3d + 3d = 6d

Sum of angles of quadrilateral = 360°.

∴ 3d + 4d + 5d + 6d = 360°
⇒ 18d = 360°
⇒ d = 20°.

Hence, the angles are

⇒ 3d = 3 × 20° = 60°

⇒ 4d = 4 × 20° = 80°

⇒ 5d = 5 × 20° = 100°

⇒ 6d = 6 × 20° = 120°.

Hence, the angles of the quadrilateral are 60°, 80°, 100°, 120°.