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The nine-pointed star shown here has a regular nonagon at its center. What is the measure of each angle at the tips of the star to the nearest .1°?
picture:
http://ezto.mheducation.com/wwtb/1259292804/chap10/sect2/prob26/92263.jpg
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1. The interior angle of a regular nonagon (9-sided regular polygon) is
= 20°*7 = 140°.
2. Hence, the exterior angle of a regular nonagon is 180° - 140° = 40°.
3. If you look into the figure under the link, you will see that the angle at the tips of the star is 180° - 40° - 40° = 100°.
Answer. The angle at the tips of the star is 100°.
