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?

1)Measure of angle POS is 25 degrees, measure of angle POQ is 40 degrees 2)Measure of angle POS is 25 degrees, measure of angle POQ is 30 degrees 3)Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees 4)Measure of angle POS is 20 degrees, measure of angle POQ is 30 degrees

Answer 1

Remark
It almost "looks like" (those are deadly words in Geometry) Meg has drawn a perpendicular bisector of PQ as well. Don't believe it. This would work if apex angle (O) was tilted either to the left or the right. And if it did tilt, it would be highly unlikely it would look lie PQ was bisected and OS was perpendicular to PQ.

She has bisected an angle at O and that's what you have to look for. That means That POS is 1/2 the size of POQ. So all you have to do is find a statement that makes this clear.

Bisect means cut in half just to be clear.

A
If the measure of POS was 25 then POQ would have to be 50. It isn't. A is wrong.

B
Same problem with the second one. POS = 25 means that POQ must be 50. It isn't. B is false.

C
This is the correct answer. If POS = 20 then POQ = 40. which it does.

D
D is wrong if C is right. You can supply the if statement.

C <<<<< Answer.