Question

a regular decagon is shown. what is the sum, in degrees, of the interior angle measures of the decagon?

Explanation:

Step1: Recall the formula

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

Step2: Identify the number of sides

A decagon has $n = 10$ sides.

Step3: Calculate the sum

Substitute $n = 10$ into the formula: $S=(10 - 2)\times180^{\circ}=8\times180^{\circ}=1440^{\circ}$.

Answer:

$1440^{\circ}$