Question

Interior and Exterior Angle polygons. I need help to find the measure of a regular decagon. To find each interior angle and to find each exterior angle

Answer 1

Answer:

• interior: 144°
• exterior: 36°

Step-by-step explanation:

It may be easiest to remember that the sum of exterior angles of any convex polygon is always 360°.

Your decagon has a sum of exterior angles that is 360°. Since it is a regular 10-sided polygon, each one is 1/10 that value: 36°.

The measure of each exterior angle is 36°.

The measure of an interior angle is the supplement of the exterior angle. Each interior angle of the regular 10-sided polygon will be ...

... 180° -36° = 144°

The measure of each interior angle is 144°.

_____

A formula often used for the sum of the measures of the interior angles is ...

... interior angle total = (n -2)×180°

For a 10-sided figure, the interior angle total is ...

... (10 -2)×180° = 1440°

When this sum is divided into 10 equal angles, the measure of one interior angle is ...

... 1440°/10 = 144° . . . . . agrees with the above computation

The exterior angle measure is the supplement of this:

... 180° -144° = 36° . . . . . exterior angle measure; agrees with the above computation