Final answer:
Using angle relationships and the fact that PR bisects angle QPN, we can determine that line MN is parallel to line PR by the Alternate Interior Angles Theorem and the concept that angles on a straight line sum to 180 degrees.
Step-by-step explanation:
To prove that line MN is parallel to line PR, we must use the information given that line MPQ, angle 1 equals angle 3, and line PR bisects angle QPN.
The fact that PR bisects angle QPN means that the two angles it creates are congruent. Since angle 1 is given to be equal to angle 3, and we know that angles on a straight line sum up to 180 degrees, we can conclude that if we add the measure of angle 1 or angle 3 to the bisected angles created by PR on line QPN, it will also sum up to 180 degrees, demonstrating that MN is parallel to PR by the Alternate Interior Angles Theorem. Because we are discussing parallel lines and angle relationships, option a.
PRN is a straight angle, would imply that line MN is parallel to PR as straight angles are indicative of a straight line, which by definition would be parallel to any other line that lies on the same plane and never intersects it.