Question

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

Answer 1

Let the required angles be (a - 15)^o, (a - 5)^o, (a + 5)^o and (a + 15)^o, as the common difference is 10 (given).
Then (a - 15)^o + (a - 5)^o + (a + 5)^o + (a + 15)^o = 360^o
⇒ 4a = 360
⇒ a = 90

Hence, the required angles of a quadrilateral are $\left(90-15\right)°,\left(90-5\right)°,\left(90+5\right)°\mathrm{and}\left(90+15\right)°;\mathrm{or}75°,85°,95°\mathrm{and}105°.$