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. 20°
c. 10°
d. 18°

Explanation:

Step1: Recall rotation symmetry of regular polygons

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

Step2: Calculate the rotation angle for 18 - sided polygon

Here, \( n = 18 \). Substitute \( n = 18 \) into the formula \(\frac{360^\circ}{n}\). So we have \(\frac{360^\circ}{18}=20^\circ\). This means that when the 18 - sided regular polygon is rotated by \( 20^\circ \) about its center, the image will coincide with the pre - image.

Answer:

B. \( 20^\circ \)