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: Analyze angle - bisector property

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

Step2: Check each option

For option 1: If m∠POS = 60° and m∠POQ = 120°, then m∠POQ = 2×m∠POS (since 2×60°=120°).
For option 2: If m∠POS = 50° and m∠POQ = 110°, then 2×50° = 100°≠110°.
For option 3: If m∠POS = 50° and m∠POQ = 120°, then 2×50° = 100°≠120°.
For option 4: If m∠POS = 60° and m∠POQ = 110°, then 2×60° = 120°≠110°.

Answer:

m∠POS = 60°, m∠POQ = 120°