Question

for a regular nonagon, find the measure of one interior angle. ______°

Explanation:

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

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \). A nonagon has \( n = 9 \) sides.

Step2: Calculate the sum of interior angles for a nonagon

Substitute \( n = 9 \) into the formula: \( S=(9 - 2)\times180^{\circ}=7\times180^{\circ}=1260^{\circ} \).

Step3: Find the measure of one interior angle of a regular nonagon

In a regular polygon, all interior angles are equal. So, divide the sum of interior angles by the number of sides (\( n = 9 \)): \( \text{One interior angle}=\frac{1260^{\circ}}{9}=140^{\circ} \).

Answer:

\( 140 \)