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Mathematics

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

AP

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Answer

Let the angles of quadrilateral are,

a, a + d, a + 2d, a + 3d

∴ a + (a + d) + (a + 2d) + (a + 3d) = 360°

⇒ 4a + 6d = 360°

⇒ 2(2a + 3d) = 360°

⇒ 2a + 3d = 180°

Putting value of d = 20° in above equation we get,

⇒ 2a + 3(20) = 180°

⇒ 2a + 60 = 180°

⇒ 2a = 180° - 60 = 120°

⇒ a = 60°.

Hence, angles = 60°, 80°, 100°, 120°.

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