Question

look at this diagram: if $overleftrightarrow{eg}$ and $overleftrightarrow{hj}$ are parallel lines and $mangle{jik}=114^{circ}$, what is $mangle{hi k}$?

Explanation:

Step1: Recall angle - sum property

$\angle JIK$ and $\angle HIK$ form a linear - pair. A linear - pair of angles is supplementary, meaning their sum is $180^{\circ}$.

Step2: Set up the equation

Let $m\angle HIK=x$. We know that $m\angle JIK + m\angle HIK=180^{\circ}$. Given $m\angle JIK = 114^{\circ}$, the equation becomes $114^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}-114^{\circ}$.
$x = 66^{\circ}$.

Answer:

$66$