The Angles of a Star

Many students harbor the limiting belief that mathematics problems have only one right solution. A good problem can debunk this myth by provoking a variety of solutions. The angles-of-a-star problem, illustrated in figure 1 , has produced much interesting thought and many elegant solutions from students and teachers alike. It is wonderfully easy to state: “Find the sum of the measures of the angles at the vertices of a five-pointed star.” This article shares some of that great diversity of solutions. Not all the methods presented are mathematical proofs, but each illustrates a powerful thinking strategy inspired by the challenge of the problem.