Answer:
- interior: 144°
- exterior: 36°
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°.
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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