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 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 where 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 for in this expression.
Evaluate
The sum of the interior angles of a decagon is Now, recall that a regular polygon is a polygon in which all the angles have the same measure. Therefore, a regular decagon has angles with the same measure. To find the measure of one angle, we will divide the sum of the angles by