Question

3 lines are shown. A line with points P, R, N intersects a line with points O, R, M at point R. A line extends from point R to point L in between angle M R P. Marcus states that angle ORP and angle LRP are a linear pair. Which best describes his statement?

Answer 1

He is incorrect. Ray RO and ray RL are not opposite rays.

Explanation:

Marcus is incorrect. In order for angles to be a linear pair, the rays of the angles that don't have a common side point, need to be opposite. This is not true for rays RO and RL, so Marcus's statement is not true.

Answer 2

Marcus is wrong.

Explanation:

As we see from the figure the angles ORP and PRM makes 180 degrees or are supplementary angles.

Marcus is wrong because a linear pair has a sum equal to 180 degrees.

But if we observe carefully the angles ORP and LRP don not together make an angle of 180 degrees. Also these angles do not have opposite rays .

Therefore angles PRM and ORP are linear pair angles but angle ORP and angle LRP are not a linear pair.

These angles do not have opposite arms as uncommon sides .

The linear pair must have

1) 180 degrees

2) opposite rays as uncommon sides

3) common vertex