The number of sides of a regular polygon where each exterior angle has a measure of 45° is

Options

A. 8
B. 10
C. 4
D. 6

Answer

To find the number of sides of a regular polygon where each exterior angle measures 45°, we can use the formula for the exterior angle of a regular polygon:

**Step 1: Understand the formula for the number of sides.**
The formula to calculate the number of sides (n) of a regular polygon based on its exterior angle (E) is:
\[ n = \frac{360°}{E} \]

**Step 2: Substitute the given exterior angle into the formula.**
In this case, the exterior angle \( E \) is given as 45°. So we substitute \( E \) into the formula:
\[ n = \frac{360°}{45°} \]

**Step 3: Perform the division.**
Now, we will divide 360 by 45:
\[ n = \frac{360}{45} \]

To simplify this, we can divide both the numerator and the denominator by 5:
- \( 360 ÷ 5 = 72 \)
- \( 45 ÷ 5 = 9 \)

So, we have:
\[ n = \frac{72}{9} \]

Now, perform the division:
\[ n = 8 \]

**Step 4: Conclusion.**
The number of sides of the regular polygon is 8. Therefore, the polygon is an octagon.