How to Measure the Interior Angles of a Star

The outer points of a five-pointed simple star have angles of 180/5=72 degrees.

The points of the familiar five-pointed star have 72-degree angles. The lines emanating from these points join up at inward-pointing points that have 108-degree angles. These angle measurements conform to the formulas for stars in general, namely that the angle of the outer points of a star are each 180/N degrees, where N is the number of points, and the inward-pointing points close to the center have angles 90 + 90/N.

Instructions

1. Count up the number of points of the star you're measuring. Denote this number by the letter N.

2. Divide 180 by N. This gives you, in degrees, the angles for the N far points of the star.

3. Divide 90 by N. Then add 90. This gives you, in degrees, the angles for the N points close to the center of the star, also known as the interior angles.

   For example, for the five-pointed star, you'd calculate 90/5 + 90 = 108.

Tips & Warnings

• These formulas hold for stars in which the points are evenly spaced and they can be connected with a pencil without lifting it from the paper. The Star of David, for example, wouldn't obey these formulas since it is composed of two overlapping triangles. The formulas also require that each point connects with the point N/2 - 0.5 positions over.

References

• Algebra: Sum of the Interior of a 5-point Star
• Sonoma College: Simple Stars