Question

select all the angles of rotation that produce symmetry for this flower.
a 45°
b 90°
c 135°
d 180°
e 225°
f 270°

Explanation:

Step1: Calculate the angle of rotational symmetry

The formula for the angle of rotational symmetry is $\frac{360^{\circ}}{n}$, where $n$ is the number of equal - parts in the figure.
Looking at the flower - like figure, assume it has 8 equal - parts. So the basic angle of rotational symmetry is $\frac{360^{\circ}}{8}=45^{\circ}$.

Step2: Find all angles of rotation that produce symmetry

If the basic angle of rotational symmetry is $45^{\circ}$, then the angles of rotation that produce symmetry are $k\times45^{\circ}$, where $k = 1,2,\cdots,8$.
When $k = 1$, the angle is $45^{\circ}$; when $k = 2$, the angle is $90^{\circ}$; when $k = 3$, the angle is $135^{\circ}$; when $k = 4$, the angle is $180^{\circ}$; when $k = 6$, the angle is $270^{\circ}$ (since $6\times45^{\circ}=270^{\circ}$).

Answer:

A. $45^{\circ}$, B. $90^{\circ}$, C. $135^{\circ}$, D. $180^{\circ}$, F. $270^{\circ}$