Question

your last streak is behind you, so lets start fresh today. my assignments high school geometry lesson 4: symmetry rotational symmetry of 2d shapes not started finding a quadrilateral from its sym... which of the following rotational symmetries apply to the regular nonagon? rotation applies to the figure? rotational symmetry of 40 about the origin yes/no rotational symmetry of 200 about the origin yes/no

Explanation:

Step1: Calculate the rotational symmetry angle of a regular nonagon

The formula for the rotational symmetry angle of a regular \(n -\)sided polygon is \(\frac{360^{\circ}}{n}\). For a nonagon, \(n = 9\), so \(\frac{360^{\circ}}{9}=40^{\circ}\). A regular nonagon has rotational symmetry of \(k\times40^{\circ}\), where \(k = 1,2,\cdots,8\)

Step2: Check the given angles

• For a rotation of \(40^{\circ}\): Since \(40^{\circ}\) is of the form \(k\times40^{\circ}\) (\(k = 1\)), a regular nonagon has rotational symmetry of \(40^{\circ}\) about the origin.
• For a rotation of \(200^{\circ}\): We can write \(200^{\circ}=5\times40^{\circ}\). Since \(5\) is an integer and \(1\leqslant5\leqslant8\), a regular nonagon has rotational symmetry of \(200^{\circ}\) about the origin

Answer:

Rotational symmetry of \(40^{\circ}\) about the origin: Yes
Rotational symmetry of \(200^{\circ}\) about the origin: Yes