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.

(n - 2) 180

$n = 9$

(9 - 2) 180

▼

Evaluate

Subtract term

(7) 180

1260

The sum of the interior angles of a nonagon is

126 0^{\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 .

Sum of Angles : One Angle : 126 0^{\circ} \frac{1 2 6 0}{9} = 14 0^{\circ}