Question

1. a regular polygon has rotational symmetry for an angle of 18°. how many sides does it have? explain.

Explanation:

Step1: Recall rotational symmetry formula

For a regular polygon with \( n \) sides, the smallest angle of rotational symmetry \( \theta \) is given by \( \theta=\frac{360^{\circ}}{n} \).

Step2: Solve for \( n \)

We know \( \theta = 18^{\circ} \), so substitute into the formula: \( 18^{\circ}=\frac{360^{\circ}}{n} \).
Multiply both sides by \( n \): \( 18^{\circ}n = 360^{\circ} \).
Divide both sides by \( 18^{\circ} \): \( n=\frac{360^{\circ}}{18^{\circ}} = 20 \).

Answer:

The regular polygon has 20 sides.