This problem is solved better well when given the drawing
or the figure. It may have been given and you forgot to attach it in the
question. However, so that we can solve this now, I drew the figure on my own
(see the attached pic).
We can see from the figure that two parallel lines are
intersected by a straight line. This type of scenario creates special angles.
Angle PXY and angle RYX are called alternate interior angles since they are on
the interior opposite sides of the cut.
By virtue of alternating interior angles, angle PXY and
angle RYX are congruent hence:
m∠RYX = m∠PXY
m∠RYX = 64.36°
