Question

The angles of a Pentagon are in arithmetic sequence. Prove that it's smallest angle is greater than 36°

Answer 1

Answer:

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Step-by-step explanation:

Sum of all angles of a regular polygon with n sides = (n-2) × 180

Let a,a + d,a + 2d,a + 3d,a + 4d are 5 terms of an AP.

Sum of all angles = 5a + 10d = (5-2) × 180 = 540

∴ a + 2d = 108

The minimum angle will be obtained when a = d.

a + 2a = 3a = 108

∴ a = 36 is the minimum angle.

Answer 2

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