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)


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