The angles of quadrilateral are in A.P., whose common difference is 10°. Find the angles.

Let the four angles of the quadrilateral be in A.P. with common difference 10° be:

a, a + 10°, a + 20°, a + 30°

The sum of the interior angles of any quadrilateral is always 360°.

⇒ a + a + 10° + a + 20° + a + 30° = 360°

⇒ 4a + 60° = 360°

⇒ 4a = 360° - 60°

⇒ 4a = 300°

⇒ a = $\dfrac{300°}{4}$

⇒ a = 75°

⇒ a + 10° = 75° + 10° = 85°

⇒ a + 20° = 75° + 20° = 95°

⇒ a + 30° = 75° + 30° = 105°.

Hence, the angles of quadrilateral are 75°, 85°, 95°, 105°.