Question

1. a regular pentagon is shown in the diagram below

image of a regular pentagon with center labeled a

if the pentagon is rotated clockwise around its center, the minimum number of degrees it must be rotated to carry the pentagon onto itself is
(1) ( 54^circ )
(2) ( 72^circ )
(3) ( 108^circ )
(4) ( 360^circ )

Explanation:

Step1: Recall rotational symmetry formula

For a regular \( n \)-sided polygon, the minimum rotation angle to map it onto itself is given by \( \frac{360^\circ}{n} \).

Step2: Identify \( n \) for pentagon

A regular pentagon has \( n = 5 \) sides.

Step3: Calculate the rotation angle

Substitute \( n = 5 \) into the formula: \( \frac{360^\circ}{5} = 72^\circ \).

Answer:

(2) \( 72^\circ \)