Question

the angle of a quadrilateral are in A.P.If the greatest angle is 120 degree than find the smaller angle​

Answer 1

Suppose the angles of quadrilateral be (a – 3d)°, (a – d)°, (a + d)° and (a + 3d)°.

As we know that, the sum of angles of a quadrilateral is 360°.

a – 3d + a – d + a + d + a + 3d = 360°

4a = 360°

a = 360/4

= 90°

Given as

The greatest angle = 120°

a + 3d = 120°

90° + 3d = 120°

3d = 120° – 90°

3d = 30°

d = 30°/3

= 10°

∴ The angles are:

(a – 3d)° = 90° – 30° = 60°

(a – d)° = 90° – 10° = 80°

(a + d)° = 90° + 10° = 100°

(a + 3d)° = 120°

The angles of quadrilateral in radians:

(60 × π/180) rad = π/3

(80 × π/180) rad = 4π/9

(100 × π/180) rad = 5π/9

(120 × π/180) rad = 2π/3

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