Question

1. a regular polygon has rotation symmetry for an angle of 20°. how many sides does it have? how many lines of symmetry does it have?

Explanation:

Step1: Recall rotation symmetry of regular polygon

For a regular polygon with \( n \) sides, the smallest angle of rotation symmetry is given by \( \frac{360^\circ}{n} \). We know the rotation symmetry angle is \( 20^\circ \), so we set up the equation \( \frac{360^\circ}{n}=20^\circ \).

Step2: Solve for number of sides \( n \)

To find \( n \), we can rearrange the equation: \( n = \frac{360^\circ}{20^\circ} \). Calculating this, \( \frac{360}{20}=18 \), so \( n = 18 \).

Step3: Determine lines of symmetry

A regular polygon with \( n \) sides has \( n \) lines of symmetry. Since \( n = 18 \), the number of lines of symmetry is also 18.

Answer:

The regular polygon has 18 sides and 18 lines of symmetry.