Question

10 PT QUESTION

Meg constructed triangle 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?

a. Measure of angle POS is 25 degrees, measure of angle POQ is 40 degrees
b. Measure of angle POS is 25 degrees, measure of angle POQ is 30 degrees
c. Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees
d. Measure of angle POS is 20 degrees, measure of angle POQ is 30 degrees

Answer 1

The correct option is c.

Explanation:

It is given that 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 POS=\angle QOS` (Definition of angle bisector)

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

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

`\angle POQ=2\angle POS`

It means angle POQ is twice of angle POS.

In option A, the measure of angle POS is 25 degrees, measure of angle POQ is 40 degrees.

In option B, the measure of angle POS is 25 degrees, measure of angle POQ is 30 degrees.

In option D, the measure of angle POS is 20 degrees, measure of angle POQ is 30 degrees.

In options A, B and D, the measure of angle POQ is not twice of angle POS.

In option C, the measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees

Here the measure of angle POQ is twice of angle POS. Therefore option c is correct.

Answer 2

The particular construction used will make OS the angle bisector of ∠POQ, so
.. ∠POS = (1/2)*∠POQ.

This is true for selection C.