Question

Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS as shown in the figure.
Which could be the measures of angle POS and angle POQ?

Answer 1

Well Meg has bisected angle POQ, thus angle POS = angle QOS Since the problem is only asking which could be measure of POS and angle POQ I would say 60 degrees for POQ and 30 degrees for angle POS.

Answer 2

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.

Answer 3

Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees

Submitted and verified by FLVS for Geometry.