Question

The angles of a quadrilateral are in AP whose common difference is 10°. Find the angles.

Answer 1

Let the required angles be (a – 15)°, (a – 5)°, (a + 5)° as the common difference is 10 (given).

Then (a – 15)° + (a – 5)° + (a + 5)° + (a + 15)° = 360° 

⇒ 4a = 360

⇒ a = 90

Hence, the required angles of a quadrilateral are

(90 – 15)°, (90 – 5)°, (90 + 5)° and (90 + 15)°, or 75°, 85°, 95° and 105°.