Question

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

An angle POQ is drawn. Two similar arcs intersect OP and OQ. Two more similar arcs intersect each other at a point S and a dashed line is drawn from O to S, such that OS bisects angle POQ

Which could be the measures of angle POS and angle POQ?
Measure of angle POS is 60 degrees, measure of angle POQ is 120 degrees
Measure of angle POS is 50 degrees, measure of angle POQ is 110 degrees
Measure of angle POS is 50 degrees, measure of angle POQ is 120 degrees
Measure of angle POS is 60 d