Lara constructed angle poq and then used a compass and straightedge to accurately construct line segment os, as shown in the figure below:
which could be the measures of angle pos and angle poq?

Lara has bisected the angle by placing her compass at a point on PO and OQ and then making a cross by placing her compass on these points. Bisecting an angle gives you half of the original. The angle of POS is therefore half of the angle of POQ.