Exercise 15 Page 402

We are given a stained glass window in the shape of the following regular polygon.

We are asked to find the measure of $\angle H.$ 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 hexagon, we will start by finding the sum of its interior angles. Since a hexagon is a polygon with six sides, we will substitute $6$ for $n$ in this expression. The sum of the interior angles of a hexagon is $720^{\circ }.$ Now, recall that a regular polygon is a polygon in which all the angles have the same measure. Therefore, a regular hexagon has $6$ angles with the same measure. To find the measure of one angle, we will divide the sum of the angles by $6.$ Since each interior angle of a regular hexagon has the measure of $120^{\circ },$ the measure of $\angle H$ is equal to $120^{\circ }.$ This means that D is the correct option.