Question

when an 18 - sided, regular polygon is rotated about its center, at which angle of rotation will the image of the polygon coincide with the preimage?
a. 24°
b. 10°
c. 20°
d. 18°

Explanation:

Step1: Recall rotation symmetry formula

For a regular \( n \)-sided polygon, the smallest angle of rotation (rotational symmetry) that maps the polygon onto itself is given by \( \frac{360^\circ}{n} \).

Step2: Substitute \( n = 18 \)

Here, the polygon has \( n = 18 \) sides. So, the angle of rotation is \( \frac{360^\circ}{18} \).

Step3: Calculate the angle

\( \frac{360^\circ}{18}= 20^\circ \). So, a rotation of \( 20^\circ \) (or multiples of it) will make the image coincide with the preimage.

Answer:

C. \( 20^\circ \)