Exercise 19 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 nonagon we will start by finding the sum of its interior angles. Let's substitute $9$ for $n$ in this expression. The sum of the interior angles of a nonagon is $1260^{\circ }.$ Now, recall that a regular polygon is a polygon in which all the angles have the same measure. Therefore, a regular nonagon has $9$ angles with the same measure. To find the measure of one angle, we will divide the sum of the angles by $9.$