Exercise 20 Page 403

Let's start by recalling the rule for the sum of the measures of the interior angles of a polygon.

Interior Angle Sum of a Polygon

The sum of the measures of the interior angles of a polygon is $(n-2)180,$ where $n$ represents the number of sides.

To find the measure of one interior angle of a regular decagon, we will start by finding the sum of its interior angles. Let's substitute $10$ for $n$ in this expression. The sum of the interior angles of a decagon is $1440^{\circ }.$ Now, recall that a regular polygon is a polygon in which all the angles have the same measure. Therefore, a regular decagon has $10$ angles with the same measure. To find the measure of one angle, we will divide the sum of the angles by $10.$