Question

what angle can you construct by repeatedly bisecting a 90° angle?
○ 180°
○ 60°
○ 30°
○ 22.5°

Explanation:

Step1: Recall angle bisection

Angle bisection divides an angle into two equal parts. The formula for bisecting an angle of measure \( \theta \) is \( \frac{\theta}{2} \).

Step2: First bisection of \( 90^\circ \)

Bisecting \( 90^\circ \), we get \( \frac{90^\circ}{2}=45^\circ \).

Step3: Second bisection (repeated bisection)

Bisecting \( 45^\circ \), we get \( \frac{45^\circ}{2} = 22.5^\circ \). Also, if we consider bisecting \( 90^\circ \) once to get \( 45^\circ \), then bisecting \( 45^\circ \) gives \( 22.5^\circ \). Alternatively, if we think of bisecting \( 90^\circ \) to get \( 45^\circ \), and then bisecting \( 45^\circ \) gives \( 22.5^\circ \). Also, let's check other options: \( 180^\circ \) is larger than \( 90^\circ \), so not from bisecting \( 90^\circ \). \( 60^\circ \) can't be obtained by bisecting \( 90^\circ \) (since \( 90/2 = 45 \), \( 45/2=22.5 \), \( 90/3 = 30 \) but bisection is division by 2, not 3). \( 30^\circ \) would require dividing \( 90^\circ \) by 3, but bisection is division by 2. So the angle from repeatedly bisecting \( 90^\circ \) is \( 22.5^\circ \).

Answer:

\( 22.5^\circ \) (the option with \( 22.5^\circ \))