### Stars

Star

We all know how a star looks like. The interior of a star is actually a pentagon. Let us now look at the vertices of the star. What is the sum of all the angles at the vertices?

We can generalise from there: Given a 2k+1 regular polygon, k>1, extend its edges to form a "star" pattern. What is the sum of the angles at the vertices?

## 1 Comments:

Can you also do it for the even case? I think we may do it for a "nice" regular n-gon, for n>4. Here "nice" is in the sense, you can extend the n-gon to get a star. The answer should be (n-4)pi.

Though I may be wrong :P

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