Question

look at this diagram: if $overleftrightarrow{eg}$ and $overleftrightarrow{hj}$ are parallel lines and $mangle jif = 46^{circ}$, what is $mangle hif?$

Explanation:

Step1: Recall angle - sum property

$\angle JIF$ and $\angle HIF$ are a linear - pair of angles. The sum of the measures of angles in a linear pair is $180^{\circ}$.

Step2: Set up the equation

Let $m\angle HIF=x$. We know that $m\angle JIF + m\angle HIF=180^{\circ}$. Given $m\angle JIF = 46^{\circ}$, so $46^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}-46^{\circ}$.
$x = 134^{\circ}$.

Answer:

$134$