To find the number of sides \( n \) of a regular polygon given the measure of its exterior angle, you can use the formula:
\[ \text{Exterior angle} = \frac{360°}{n} \]
From this formula, you can solve for \( n \):
\[ n = \frac{360°}{\text{Exterior angle}} \]
Now, let's apply this formula to the given exterior angles.
- For an exterior angle of \( 30° \):
\[ n = \frac{360°}{30°} = 12 \]
So, for the exterior angle of \( 30° \), the polygon has \( n = 12 \) sides.
- For an exterior angle of \( 72° \):
\[ n = \frac{360°}{72°} = 5 \]
So, for the exterior angle of \( 72° \), the polygon has \( n = 5 \) sides.
Summary:
- For \( 30° \): \( n = 12 \)
- For \( 72° \): \( n = 5 \)
3 answers