tumblr7spn
contestada

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?

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 measu class=

Respuesta :

Answer:

The answer is C

Step-by-step 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:

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

Step-by-step 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,

[tex]\angle POQ=\angle POS+\angle QOS[/tex]

[tex]\angle POS=\angle QOS[/tex]    ∴ angle bisector

[tex]\angle POQ=\angle POS+\angle POS=2\angle POS[/tex]

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°,