Question

1. a regular pentagon is shown in the diagram below. 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 a) 72° b) 360° c) 108° d) 54°

Explanation:

Step1: Recall the formula for rotational symmetry

The formula for the minimum degree of rotation \( \theta \) for a regular \( n - \)sided polygon is \( \theta=\frac{360^{\circ}}{n} \).

Step2: Identify the number of sides of the polygon

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

Step3: Calculate the rotation angle

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

Answer:

A. \( 72^{\circ} \)