Glencoe Math: Course 3, Volume 2
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Glencoe Math: Course 3, Volume 2 View details
4. Polygons and Angles
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Exercise 15 Page 402

The sum of the measures of the interior angles of a polygon is where represents the number of sides.

D

Practice makes perfect

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

Regular hexagon

We are asked to find the measure of 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 where 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 for in this expression.
Evaluate
The sum of the interior angles of a hexagon is Now, recall that a regular polygon is a polygon in which all the angles have the same measure. Therefore, a regular hexagon has angles with the same measure. To find the measure of one angle, we will divide the sum of the angles by
Since each interior angle of a regular hexagon has the measure of the measure of is equal to This means that D is the correct option.