Question

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

Answer 1

Step 1: Find the value of each exterior angle

The given geometry is a regular polygon with $10$ sides.

Thus, the number of sides, $n=10$.

It is known that the sum of all exterior angles of a polygon is $360°$.

As the given polygon is regular, so the value of each exterior angle can be given by $\left(\frac{360°}{n}\right)=\left(\frac{360°}{10}\right)=36°$.

Step 2: Find the value of each interior angle

It is known that the sum of an interior angle and the corresponding exterior angle is $180°$.

Thus, the value of each interior angle of the given regular polygon can be given by, $\left(180°-36°\right)=144°$.

Hence, the measure of each angle of a regular polygon with $10$ sides is $144°$.