Question

what is the sum of the interior angle measures of a regular decagon?
what is the measure of each interior angle of a regular decagon?

Explanation:

Step1: Use the formula for the sum of interior angles

The formula for the sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a decagon, \(n = 10\).

$$S=(10 - 2)\times180^{\circ}=8\times180^{\circ}=1440^{\circ}$$

Step2: Find the measure of each interior angle

Since the decagon is regular (all angles are equal), divide the sum of interior angles by the number of sides.

$$A=\frac{S}{n}=\frac{1440^{\circ}}{10}=144^{\circ}$$

Answer:

The sum of the interior angle measures of a regular decagon is \(1440^{\circ}\).
The measure of each interior angle of a regular decagon is \(144^{\circ}\).