SOLUTION: 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°?
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Question 1041968: 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°? Found 3 solutions by Alan3354, KMST, ikleyn:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! I do not see your star, but I think I can make three possible stars by extending the sides of the nonagon. -0.026,2.82
For an easy problem you would have one of the 3 possible stars: the one that is made by adding isosceles triangles built around the nonagon. Each one of those isosceles triangles has a side of the nonagon as its base.
The two base angles of each of those isosceles triangles are exterior angles of the nonagon.
The measure of an exterior angle of a regular polygon with sides is ,
so the measure of an exterior angle of a regular nonagon is .
So, those isosceles triangles have base angles measuring .
The other angle is at a tip of the start.
Since the sum of the measures of the angles of any triangle is ,
the angle at the tip og the star measures .
NOTE:
The other two stars have sharper tips, whose angles are not quite as easy to calculate.
Here is the smaller one: .
The larger one, with the sharpest tips is too big A partial drawing is shown below.
