Question
The ratio of the sum of interior angles of a polygon to
the sum of its exterior angles is 5 : 1. Find the number of sides of the polygon and the measure of each interior angle (for a regular polygon).Solution
Sum of exterior angles of any polygon = 360° Let sum of interior angles = S. Given: S : 360 = 5 : 1 ⇒ S = 5 × 360 = 1800° For an n-sided polygon: S = (n − 2) × 180 So (n − 2) × 180 = 1800 n − 2 = 10 ⇒ n = 12 If it is regular, each interior angle = S / n = 1800 / 12 = 150°.
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