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

Question

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: \( 20^\circ \)