Question

Lara constructed 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

Where's the figure, may I ask?

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.

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