Question

1. which regular polygon has a minimum rotation of 45° to carry the polygon onto itself?

a) octagon
b) pentagon
c) hexagon
d) decagon

Explanation:

Step1: Recall the formula for the minimum rotation angle

The formula for the minimum rotation angle of a regular polygon is $\frac{360^{\circ}}{n}$, where $n$ is the number of sides.

Step2: Substitute the given angle and solve for $n$

We are given that the minimum rotation angle is $45^{\circ}$. So, we set up the equation $\frac{360^{\circ}}{n}=45^{\circ}$. Solving for $n$, we multiply both sides by $n$ to get $360^{\circ}=45^{\circ}n$. Then divide both sides by $45^{\circ}$: $n = \frac{360^{\circ}}{45^{\circ}}=8$.

Answer:

A. octagon