If the measure of one exterior angle of a regular polygon is 36 degrees, how many sides does the polygon have?

The sum of exterior angles of ANY regular polygon is 360
degrees

This can be proved because one exterior angle and
one interior angle add up to be 180 degrees

the total
interior angle sum is 180(n-2)

the total exterior +interior
sum is
180n

180n-180(n-2)=360

In this
question, each exterior angle is 36 degrees

the total is
360 degrees

Therefore, the number of sides is 360/36= 10
sides

It is a dodecagon

The
Final answer:

The polygon has 10
sides.

this method works for any regular
polygon