Question

The angles of a quadrilateral are in A.P. with common difference 20°. Find its angles. 

Answer 1

Let the four angle of a quadrilateral in A.P. be a, a + 20°, a + 40° and a + 60°

∴ a + (a + 20°) + (a + 40°) + (a + 60°) = 360°  ...[Angle sum property]

`=>` 4a + 120° = 360°

`=>` 4a = 240°

`=>` a = 60°   ...(1)

Thus, angles of a quadrilateral are = a, a + 20°, a + 40° and 60°

= 60°, 80°, 100° and 120°