Answer in Brief

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

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#### Solution

Here, we are given that the angles of a quadrilateral are in A.P, such that the common difference is 10°.

So, let us take the angles as a - d, a, a +d, a + 2d

Now, we know that the sum of all angles of a quadrilateral is 360°. So, we get,

(a - d) + (a) + (a + d) + (a + 2d) = 360

a - d + a + a + d + a + 2d = 360

4a + 2(10) = 360

4a = 360 - 20

On further simplifying for a we get

a = 85

So the first angle is given by

a - d = 85 - 10

= 75°

Second angle is given by

a = 85°

Third angle is given by

a + d = 85 + 10

= 95°

Fourth angle is given by,

a + 2d = 85 + (2)(10)

= 85 + 20

= 105°

Therefore, the four angles of the quadrilateral are 75°, 85°, 95°, 105°

Concept: Arithmetic Progression

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