Exercise 5 Page 483

The square that occupies $\angle JMK$ tells us it is a right angle and thus $90^{\circ }.$ Since this angle forms a linear pair with $\angle GMK,$ they are supplementary angles, and add up to $180^{\circ }.$ Therefore, by the Right Angles Congruence Theorem, $m\angle GMK$ also has to be $90^{\circ }\text{:}$

Since these angles have the same measure, they are congruent: Finally, we also see that $MG$ and $MJ$ as well as $ML$ and $MH$ forms opposite rays. Therefore, by the Vertical Angles Congruence Theorem, we can conclude that