Question

for each figure below, determine if it has rotational symmetry.
if it does, give the smallest angle of rotation needed for the figure to appear unmoved.

rotational symmetry? ○ yes ○ no
angle? □°

rotational symmetry? ○ yes ○ no
angle? □°

Explanation:

Step1: Analyze the sun-like figure

Count the number of triangular points: there are 10 identical points evenly spaced around the circle. The smallest rotation angle is calculated by dividing the full circle (360°) by the number of symmetric parts.
$\text{Angle} = \frac{360^\circ}{10} = 36^\circ$
This figure maps onto itself when rotated by this angle, so it has rotational symmetry.

Step2: Analyze the right triangle

A non-isosceles right triangle cannot be rotated by any angle less than 360° and appear unchanged, as its sides and angles are not symmetrically arranged.

Answer:

1. Sun-like figure: Rotational symmetry? Yes, Angle? $36^\circ$
2. Right triangle: Rotational symmetry? No, Angle: (N/A)