Question

The angles of a quadrilateral are in AP whose common difference is ${10}^{\circ }$ find the angle.

Answer 1

Since the angles are in A.P., let the angles are p, p+10, p+20, p+30
sum of angles=360
⇒ p + p+10 + p+20 + p+30 = 360
⇒ 4p + 60 = 360
⇒ 4p = 360-60 = 300
⇒ p = 300/4 = 75

So the angles are
p = 75
p+10 = 75+10 = 85
p+20 = 75+20 = 95
p+30 = 75+30 = 105