Question

Beck used a compass and straightedge to accurately construct line segment OS as shown in the figure.

Answer 1

Based on the given figure above, we can find the measures of angle POS and angle POQ by analyzing it carefully. Look for POS and POQ where POS = 1/2 POQ. Base on this, we can conclude that measure of angle POS = 60° and measure of angle POQ = 120°. Therefore, the answer would be option A. 

Answer 2

Observe the figure below.

The given figure shows that the construction of line segment OS. We can observe clearly that OS is bisector of angle POS.

The bisector divides the angle into two equal angles.

So, $\angle POS = \frac{1}{2} \angle POQ$

Let us observe the given options.

In first option, $60^\circ = \frac{1}{2} \times 120^\circ$

Therefore, $m \angle POS = 60^\circ, m \angle POQ=120^\circ$

So, Option A is the correct answer.