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in Arithmetic Progression by (49.4k points)
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The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.

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Best answer

Let the angles be (a – 3d), (a – d), (a + d) and (a + 3d)

a – 3d + a – d + a + d + a + 3d = 360° (sum of angles of quadrilateral)

4a = 360°

a = 90°

According to question,

(a + d) – (a – d) = 10°

2d = 10°

d = 5°

Therefore,

(a – 3d) = 90° – 15° = 75°

(a – d) = 90° – 5° = 85°

(a + d) = 90° + 5° = 95°

(a + 3d) = 90° + 15° = 105°

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