Question

look at this diagram: if (overleftrightarrow{eg}) and (overleftrightarrow{hj}) are parallel lines and (mangle jif = 49^{circ}), what is (mangle hif?)

Explanation:

Step1: Recall linear - pair property

Adjacent angles on a straight - line are supplementary. $\angle JIF$ and $\angle HIF$ form a linear pair.

Step2: Set up the equation

Let $m\angle JIF = 49^{\circ}$ and $m\angle HIF=x$. Since $\angle JIF+\angle HIF = 180^{\circ}$ (linear - pair angles), we have the equation $49^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}-49^{\circ}$.
$x = 131^{\circ}$.

Answer:

$131$