A light directed from point $E$ is pointed at a hinged mirror with right angle as shown at right.  

1. If $∠x$ measures $36°$, find the measures of $∠a$, $∠r$, $∠m$, $∠y$, and $∠z$.

   Hint (a):

   When the light hits the mirror the angle of incidence and angle of reflection are congruent. Therefore $∠x=∠a$

   Answer (a):

   $∠a=36°$, $∠r=54°$, $∠m=54°$, $∠y=72°$, $∠z=108°$

2. Why must the arrows at points $A$ and $E$ be parallel?

   Hint (b):

   Use the angle measurements found to explain why the arrows at points $A$ and $E$ must be parallel.