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Find the measure of each interior angle of a regular polygon of $10$ sides.

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Answer:

$144 ^ \circ$

Step by Step Explanation:

1. We know that the sum of all exterior angles of a polygon is $360 ^ \circ.$
2. Each exterior angle of a regular polygon of $10$ sides $= { \Bigg ( \dfrac{ 360 } { 10 } \Bigg ) } ^ \circ = 36 ^ \circ.$
3. Thus, each interior angle of a regular polygon of $10$ sides $= 180 ^ \circ - 36 ^ \circ = 144 ^ \circ$.

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