Question

determine the minimum rotation (in degrees) which will carry the following figure onto itself (where all sides and vertices will match up). assume this is a regular polygon. round to the nearest tenth if necessary.
options: 88°, 74°, 72°, 51°, 81°, 86°

Explanation:

Step1: Identify the polygon type

The figure is a regular pentagon, so it has \( n = 5 \) sides.

Step2: Recall the formula for rotational symmetry

The minimum angle of rotation \( \theta \) for a regular polygon is given by \( \theta=\frac{360^{\circ}}{n} \).

Step3: Substitute \( n = 5 \) into the formula

\( \theta=\frac{360^{\circ}}{5} = 72^{\circ} \).

Answer:

\( 72^{\circ} \) (corresponding to the option \( 72^{\circ} \))