Question

in the figure below, $overrightarrow{fk}$ is parallel to $overrightarrow{lq}$ and $overrightarrow{mh}$ is parallel to $overrightarrow{oj}$. $overrightarrow{mh}$ intersects $overrightarrow{lq}$ and $overrightarrow{fk}$ at $n$ and $g$, respectively. $overrightarrow{oj}$ intersects $overrightarrow{lq}$ at $p$ and $overrightarrow{fk}$ at $i$. which of the following must be true? a $x = y$ b $x = 2y$ c $x - y=90$ d $x + y = 180$

Explanation:

Step1: Identify corresponding - angles

Since $\overrightarrow{FK}\parallel\overrightarrow{LQ}$ and $\overrightarrow{MH}\parallel\overrightarrow{OJ}$, $\angle x$ and $\angle y$ are corresponding angles.

Step2: Apply the property of parallel - lines

For two parallel lines cut by a transversal, corresponding angles are equal. So $x = y$.

Answer:

A. $x = y$