Question

beck 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? m∠pos = 60°, m∠poq = 120° m∠pos = 50°, m∠poq = 110° m∠pos = 50°, m∠poq = 120° m∠pos = 60°, m∠poq = 110°

Explanation:

Step1: Recall angle - bisector property

If OS is constructed using a compass and straight - edge, it is likely an angle - bisector of ∠POQ. So, m∠POQ = 2m∠POS.

Step2: Check each option

For option A: If m∠POS = 60°, then 2m∠POS=2×60° = 120° which is equal to m∠POQ.
For option B: If m∠POS = 50°, then 2m∠POS = 100°≠110°.
For option C: If m∠POS = 50°, then 2m∠POS = 100°≠120°.
For option D: If m∠POS = 60°, then 2m∠POS = 120°≠110°.

Answer:

A. m∠POS = 60°, m∠POQ = 120°