Question

marcus states that angle orp and angle lrp are a linear pair which best describes his statement? he is correct. the angles share a common vertex so they are a linear pair he is correct. the angles share a common ray so they are a linear pair he is incorrect. angle orp does not form a linear pair with another angle in the diagram he is incorrect ray ro and ray rl are not opposite rays

Explanation:

Step1: Recall the definition of a linear pair

A linear pair of angles is formed when two adjacent angles have their non - common sides as opposite rays.

Step2: Analyze angle ORP and angle LRP

For angles \( \angle ORP\) and \( \angle LRP\), the non - common sides are \( \overrightarrow{RO}\) and \( \overrightarrow{RL}\). Since \( \overrightarrow{RO}\) and \( \overrightarrow{RL}\) are not opposite rays (opposite rays lie on the same straight line and point in opposite directions), the two angles \( \angle ORP\) and \( \angle LRP\) do not form a linear pair.
The first two options are wrong because just sharing a common vertex (\(R\)) or a common ray (\(\overrightarrow{RP}\)) is not sufficient for a linear pair. The third option is too general. The key reason is the non - opposite nature of the non - common rays.

Answer:

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