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�?

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!
Shown where?
Answer by KMST(5328)   (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.

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Also solved in
https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.1042073.html

https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.1042073.html

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