2. Find the measure of an interior angle and an exterior angle of a regular 17-gon. (round answers to the nearest tenth of a degree)
Answer : interior angle =158.8
Exterior angle = 21.2
How do I show work
To find the measure of an interior angle and an exterior angle of a regular 17-gon, you can use the formula for the measure of an interior angle of a regular polygon:
Interior angle = (n-2) * 180/n
where n is the number of sides of the polygon.
In this case, n = 17, so the measure of an interior angle of the regular 17-gon is:
Interior angle = (17-2) * 180/17
= 158.8°
The measure of an exterior angle of a regular polygon is equal to the measure of an interior angle divided by the number of sides.
In this case, the measure of an exterior angle of the regular 17-gon is:
Exterior angle = 158.8°/17
= 21.2°
Therefore, the measure of an interior angle and an exterior angle of a regular 17-gon is 158.8° and 21.2° respectively.