Question

. Find the measure of each interior angle of a regular polygon having (i) 10 sides (ii) 15 sides
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Answer 1

The sum of the measures of the interior angles of a decagon (10 sided polygon) is 1,440. We found this by using the formula (n-2)(180). Thus, to find the measure of each interior angle we simply divide the sum by the number of total sides in the polygon. 1,440/10 = 144.

Since the 15-gon is regular, this total is shared equally among the 15 interior angles. Each interior angle must have a measure of 2340 ÷ 15 = 156 degrees.

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