Each interior angle of a regular polygon is 108 degrees How many sides does the polygon have?

For a regular polygon, all sides are equal, and all interior angles are equal.

Take any two angles, add them: 108+108=216

A circle always has a total of 360 degrees.

Subtract the sum of the two angles from 360: 360-216=144

The sum of remaining angles must total 144.

It takes two sides to form an angle, therefore we divide by 2: 144/2=72

Now we divide the circle by 72: 360/72=5 sides.

We see it is a pentagon. The sum of the angles in a pentagon is always 540.

Therefore we can check our work: 540/5=108 (our original known angle!)