Question

a regular 10 - sided polygon is shown.
what is the measure of one of its interior angles?
a 144°
b 180°
c 1440°
d 1800°

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 \( S=(n - 2)\times180^{\circ} \). For a 10 - sided polygon, \( n = 10 \). So we calculate the sum of interior angles first: \( S=(10 - 2)\times180^{\circ}=8\times180^{\circ} = 1440^{\circ} \).

Step2: Find the measure of one interior angle

In a regular polygon, all interior angles are equal. So to find the measure of one interior angle, we divide the sum of interior angles by the number of sides \( n \). For a regular 10 - sided polygon, the measure of one interior angle \( \theta=\frac{1440^{\circ}}{10}=144^{\circ} \).

Answer:

A. \( 144^{\circ} \)