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

Question

The angles of a quadrilateral are in A.P. whose common difference is 10&deg;. Find the angles.

Philoid · Accepted Answer

Let the angles be (a – 3d), (a – d), (a + d) and (a + 3d)

a – 3d + a – d + a + d + a + 3d = 360^o (sum of angles of quadrilateral)

4a = 360^o

a = 90^o

According to question,

(a + d) – (a – d) = 10^o

2d = 10^o

d = 5^o

Therefore, (a – 3d) = 90^o – 15^o = 75^o

(a – d) = 90^o – 5^o = 85^o

(a + d) = 90^o + 5^o = 95^o

(a + 3d) = 90^o + 15^o = 105^o