Question

Meg constructed triangle POQ and then used compass and straight edge to accurately construct line segment OS, as shown in the figure below. Which could be a measure of POS and angle POQ?

Answer 1

The answer is C

Explanation:

The measurement of angle POS is 20 and POQ is 40

OS is an angle bisector of ∠POQ. This means it splits ∠POQ into two congruent pieces.

This tells us that ∠POS+∠SOQ = ∠POS+∠POS = ∠POQ.

If m∠POS = 20, this means that m∠POQ = 20+20 = 40°.

Answer 2

The correct option is C) m∠POS = 20°, m∠POQ = 40°,

Explanation:

Consider the provided figure.

Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS.

From the given figure it is clear that OS is angle bisector of POQ,

`\angle POQ=\angle POS+\angle QOS`

`\angle POS=\angle QOS` ∴ angle bisector

`\angle POQ=\angle POS+\angle POS=2\angle POS`

Thus, the measure of ∠POQ is double the measure of ∠POS.

There is only one option in which m∠POQ is double the m∠POS.

Therefore, the correct option is C) m∠POS = 20°, m∠POQ = 40°,