Question

which of the following transformations carry this regular polygon onto itself?
rotation of 36°
counterclockwise
rotation of 40°
counterclockwise
reflection across l
rotation of 60°
counterclockwise

Explanation:

Step1: Calculate the rotational symmetry angle

For a regular polygon with \(n\) sides, the angle of rotational symmetry is \(\frac{360^{\circ}}{n}\). The given polygon is a non - agon (\(n = 9\)), so \(\frac{360^{\circ}}{9}=40^{\circ}\). A rotation of \(40^{\circ}\) (or multiples of \(40^{\circ}\)) will map the non - agon onto itself.

Step2: Analyze reflection

A reflection across a line of symmetry (such as the line \(l\) which is a line of symmetry for the non - agon) will also map the polygon onto itself.

Answer:

rotation of \(40^{\circ}\) counterclockwise, reflection across \(l\)