Final answer:
The question appears to be related to geometry and involves concepts such as parallel lines and perpendicularity. However, without a clear diagram or sufficient information, it's impossible to provide a complete proof for the statement "MN || PR".
Step-by-step explanation:
The student's question seems to involve proving relationships between angles and lines which imply a context of geometry, specifically involving parallel lines, angle bisectors, and perpendicular lines.
However, the information provided does not clearly present a geometric figure or a comprehensive set of relationships needed to prove a statement like "MN || PR". Therefore, without a clear description of the figure or additional given information, it is impossible to provide an accurate proof or solution to the student's inquiry.
The student may be referencing the concept that if a transversal intersects two lines such that a pair of corresponding angles are equal, then the lines are parallel (Alternate Interior Angles Theorem). Proof of such would generally require a diagram and a set of given angles and lines. However, due to a lack of a clear diagram or description in this case, a step-by-step solution cannot be formulated.