Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS as shown in the figure.
(the figure for this will be in the comments)

Question

Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS as shown in the figure. 
(the figure for this will be in the comments)

anonymous · Answer

attachment

anonymous · Answer

Which could be the measures of angle POS and angle POQ?

anonymous · Answer

dang its not working nvm guise

directrix · Answer

The construction portrayed in the graphic is that of the construction of an angle bisector. Recall that all points on an angle bisector are equidistant from the sides of the angle.
<POS and <SOQ have the same measure - they are congruent angles. Therefore, the measure of angle POQ is twice the measure of angle POS.
@jessie04

anonymous · Answer

Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees Submitted and verified by FLVS for Geometry.