Question

question 5 (multiple choice worth 1 points) (01.02r 01.06r lc) lara constructed ∠poq and then 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 35°, m∠poq 65° m∠pos 40°, m∠poq 70° m∠pos 45°, m∠poq 75° m∠pos 30°, m∠poq 60°

Explanation:

Step1: Recall angle - bisector property

If OS is the angle - bisector of ∠POQ, then m∠POS=\frac{1}{2}m∠POQ.

Step2: Check each option

For option 1: If m∠POS = 35° and m∠POQ=65°, then \frac{1}{2}m∠POQ=\frac{65^{\circ}}{2}=32.5^{\circ}
eq35^{\circ}.
For option 2: If m∠POS = 40° and m∠POQ = 70°, then \frac{1}{2}m∠POQ=\frac{70^{\circ}}{2}=35^{\circ}
eq40^{\circ}.
For option 3: If m∠POS = 45° and m∠POQ = 75°, then \frac{1}{2}m∠POQ=\frac{75^{\circ}}{2}=37.5^{\circ}
eq45^{\circ}.
For option 4: If m∠POS = 30° and m∠POQ = 60°, then \frac{1}{2}m∠POQ=\frac{60^{\circ}}{2}=30^{\circ}.

Answer:

m∠POS = 30°, m∠POQ = 60°