Each exterior angle of a regular polygon measures 9°. How many sides does the polygon have?Choices:- 36 45 40 30

1. Break Down the Problem

To find the number of sides $n$ of a regular polygon given the measure of each exterior angle, we can use the relationship between the exterior angle and the number of sides of the polygon.

2. Relevant Concepts

The exterior angle $E$ of a regular polygon is related to the number of sides $n$ by the formula:

$E = \frac{360°}{n}$

3. Analysis and Detail

Given that $E = 9°$, we can set up the equation:

$9° = \frac{360°}{n}$

To solve for $n$, we will rearrange the formula:

$n = \frac{360°}{9°}$

4. Verify and Summarize

Now, performing the calculation:

$n = \frac{360}{9} = 40$

Thus, the regular polygon has $40$ sides.

Final Answer

The polygon has 40 sides.