Question

The angles of a quardilateral are in A.P. The greatest angle is thrice ithe least angle. Find the greatest angle.

Answer 1

Answer:

greatest angle = 135°

Step-by-step explanation:

let smaller angle be x

angles are in A.P.

therefore, let angles be a,a+d,a+2d and a+3d

a+a+d+a+2d+a+3d = 360....(sum of measure of all angles of quadrilateral)

4a + 6d = 360

2a + 3d = 360......(1)

a+3d = 3a......(2)

3d = 3a - a

3d = 2a

2a - 3d = 0......(3)

adding eq.(1) and (3)

therefore, a = 45

from eq.(2)

a+3d = 3a

= 3(45)

= 135