Question

1. which of the following would not be an angle of rotational symmetry about the center of a regular octagon? (1) 90° (2) 135° (3) 245° (4) 315°

Explanation:

Step1: Calculate the measure of central angle

The measure of the central angle of a regular octagon is $\frac{360^{\circ}}{8} = 45^{\circ}$.

Step2: Check divisibility

An angle of rotational symmetry must be a multiple of $45^{\circ}$.

• For $90^{\circ}$: $90\div45 = 2$ (a multiple).
• For $135^{\circ}$: $135\div45=3$ (a multiple).
• For $245^{\circ}$: $245\div45=\frac{49}{9}$ (not a multiple).
• For $315^{\circ}$: $315\div45 = 7$ (a multiple).

Answer:

(3) $245^{\circ}$