**Star
angles **

What's the sum of the measures of the angles at the vertices of a five-pointed
star? (Alan Lipp, "The Angles of a Star,"* Mathematics Teacher*
93, 6, September, 2000)

**Approaches**

Experiment with geometry software.

Imagine walking and turning.

reflex angle

Exterior angles: around one small triangle, angles equal sum of angles of star

Inscribe regular one in circle (assuming the sum is the same for all); angles subtended.

Move one vertex to nearby one; angle at target becomes sum, other angle drops to 0; move that line, to make triangle with same angle sum

Draw AC. The vertical angles at F are congruent, so 1 + 2 = 3 + 4. Therefore the sum of the star's angles equals sum of the angles in triangle ABC.

**Your
experience**

Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!

*Last updated 30 November, 2004*