Q11 of 50 Page 26

The angles of a pentagon are in arithmetic sequence. Prove that its smallest angle is greater than 36°.

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.


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