In the diagram, $M N P Q$ is a rectangle with points $M, N, P$, and $Q$ on the sides of $\triangle X Y Z$, as shown. If $\angle Z N M=68^{\circ}$ and $\angle X Y Z=55^{\circ}$, what is the measure of $\angle Y X Z$ ?
(A) $77^{\circ}$
(B) $113^{\circ}$
(D) $97^{\circ}$
(E) $103^{\circ}$
(C) $93^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-050.jpg?height=247&width=608&top_left_y=1652&top_left_x=1062)
Since $M N P Q$ is a rectangle, then $\angle N M Q$ is a right angle and thus so is $\angle N M Z$. The sum of the angles in $\triangle N M Z$ is $180^{\circ}$, so

![](https://cdn.mathpix.com/cropped/2024_04_20_33a8a6559d675f59baa2g-098.jpg?height=374&width=1136&top_left_y=1987&top_left_x=554)

Since the sum of the angles in $\triangle Z X Y$ is also $180^{\circ}$, then

$$
\angle Y X Z=180^{\circ}-\angle X Z Y-\angle X Y Z=180^{\circ}-22^{\circ}-55^{\circ}=103^{\circ}
$$

ANSWER: (E)