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Question

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

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Solution

The angles of quadrilateral are in A.P. with common difference, d = 20

Let the first angle be 'a'

Then,

Second angle = a + d = a + 20

Third angle = a + 2d = a + 40

Fourth angle = a + 3d = a + 60

We know that the sum of all angles of a quadrilateral is 360

a + a+20 + a+40 + a+60 = 360

4a + 120 = 360

4a = 360 - 120

4a = 240

a = 2404

a = 60

First angle = 60

Second angle = 60 + 20 = 80

Third angle = 60 + 40 = 100

Fourth angle = 60 + 60 = 120

Hence, the angles of given quadrilateral are 60, 80, 100, 120


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