
To find: measure of exterior

Answer to Problem 10ST2
In a regular decagon, the sum of the measures of the exterior angles is
Explanation of Solution
Given information: Name of given
First find measure of each exterior angle.
Le n denotes number of sides of a regular decagon.
Number of sides in a regular decagon
Consider the following figure of decagon.
This figure consists of 10
So,
Sum of angles in 10 triangles is equal to
Sum of angles at the center of the decagon forms a complete angle that is angle equal to
So,
Sum of interior angles of a decagon is equal to
Now,
Measure of each interior angle is equal to sum of interior angles divided by number of sides
Measure of each interior angle is equal to
To find measure of each exterior angle, use the following formula.
Measure of each exterior angle
Put
So,
Measure of each exterior angle
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