Question

Find the measure of an exterior angle of each regular polygon.

A pentagon
°

36-gon
°

18-gon
°

Answer 1

To find the measure of an exterior angle of a regular polygon, you can use the formula:

\[
\text{Exterior Angle} = \frac{360^\circ}{n}
\]

where \( n \) is the number of sides of the polygon.

1. **Pentagon (n=5)**:
\[
\text{Exterior Angle} = \frac{360^\circ}{5} = 72^\circ
\]

2. **36-gon (n=36)**:
\[
\text{Exterior Angle} = \frac{360^\circ}{36} = 10^\circ
\]

3. **18-gon (n=18)**:
\[
\text{Exterior Angle} = \frac{360^\circ}{18} = 20^\circ
\]

Thus, the measures of the exterior angles are:
- Pentagon: \( 72^\circ \)
- 36-gon: \( 10^\circ \)
- 18-gon: \( 20^\circ \)