Question

explain how you would find the angles of rotational symmetry for the figure shown. the figure has rotational symmetry at the angles that map one of the petals in the dropdown layer to the dropdown position. since there are blank such petals and 360° ÷ blank = blank°, the angles occur at multiples of blank°.

Explanation:

Step1: Analyze the figure's petals

The figure (a flower - like shape) has a certain number of petals. Let's assume the outer (or a particular) layer has, say, 8 petals (by visually inspecting the flower - like figure, it seems to have 8 symmetric parts). So the first blank (number of petals) is 8.

Step2: Determine the mapping position

When finding rotational symmetry, we map one petal to the next (adjacent) position. So the first dropdown (layer, say outer) and the second dropdown (position, say next).

Step3: Calculate the rotational angle

The formula for the angle of rotational symmetry (the basic angle) is $\frac{360^{\circ}}{n}$, where $n$ is the number of symmetric parts (petals here). If $n = 8$, then $\frac{360^{\circ}}{8}=45^{\circ}$. So $360\div8 = 45$, and the angles occur at multiples of $45^{\circ}$.

Answer:

The figure has rotational symmetry at the angles that map one of the petals in the \(\boldsymbol{\text{outer}}\) layer to the \(\boldsymbol{\text{next}}\) position. Since there are \(\boldsymbol{8}\) such petals and \(360^{\circ}\div\boldsymbol{8}=\boldsymbol{45}^{\circ}\), the angles occur at multiples of \(\boldsymbol{45}^{\circ}\)