Question

36 for a regular polygon with 10 sides, find the measure of each individual interior angle: (remember, all interior angles in regular polygons are congruent) each interior angle = degrees.

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The sum of the interior angles of a polygon with \( n \) sides is given by the formula \( S=(n - 2)\times180^{\circ} \). For a 10 - sided polygon, \( n = 10 \).
So, we substitute \( n = 10 \) into the formula: \( S=(10 - 2)\times180^{\circ}=8\times180^{\circ}=1440^{\circ} \).

Step2: Find the measure of each interior angle

Since a regular polygon has all interior angles congruent, to find the measure of each interior angle, we divide the sum of the interior angles by the number of sides \( n \).
The formula for each interior angle \( I \) of a regular polygon is \( I=\frac{(n - 2)\times180^{\circ}}{n} \).
Substituting \( n = 10 \) into the formula: \( I=\frac{(10 - 2)\times180^{\circ}}{10}=\frac{1440^{\circ}}{10} = 144^{\circ} \).

Answer:

\( 144 \)