Question

question 5 multiple choice worth 1 points 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?

Explanation:

1. Assume OS is an angle - bisector (a common construction with compass and straight - edge):

• If OS is the angle - bisector of \(\angle POQ\), then \(\angle POQ = 2\angle POS\).

1. Check each option:

• Option A: If \(\angle POS=30^{\circ}\) and \(\angle POQ = 60^{\circ}\), then \(2\times\angle POS=2\times30^{\circ}=60^{\circ}=\angle POQ\).
• Option B: If \(\angle POS = 40^{\circ}\) and \(\angle POQ=70^{\circ}\), then \(2\times40^{\circ}=80^{\circ}

eq70^{\circ}\).

• Option C: If \(\angle POS = 45^{\circ}\) and \(\angle POQ = 75^{\circ}\), then \(2\times45^{\circ}=90^{\circ}

eq75^{\circ}\).

• Option D: If \(\angle POS = 32^{\circ}\) and \(\angle POQ = 50^{\circ}\), then \(2\times32^{\circ}=64^{\circ}

eq50^{\circ}\).

Answer:

A. \(\angle POS = 30^{\circ},\angle POQ = 60^{\circ}\)