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Complete.

10. In a regular decagon, the sum of the measures of the exterior angles is?¯ and the measure of each interior angle is ?¯.

Short Answer

Expert verified

In a regular decagon, the sum of the measures of the exterior angles is360°and the measure of each interior angle is144°.

Step by step solution

01

Step 1. Description of step.

In a decagon, the number of sides are 10.

Therefore, the value of n is 10.

02

Step 2. Description of step.

The sum of the measures of exterior angles of a polygon is360°.

Therefore, the sum of the measures of exterior angles of a decagon is 360°.

03

Step 3. Description of step.

The measure of each interior angle of a regular polygon with n sides is given by n2180°n.

Therefore, the measure of each interior angle of a regular polygon with 10 sides is given by:

102180°10=8×180°10=8×18°=144°

04

Step 4. Write the complete statement.

In a regular decagon, the sum of the measures of the exterior angles is 360° and the measure of each interior angle is 144°.

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