Question

look at this diagram: if $overleftrightarrow{eg}$ and $overleftrightarrow{hj}$ are parallel lines and $mangle gfd = 129^{circ}$, what is $mangle gfi$?

Explanation:

Step1: Identify angle - relationship

$\angle GFD$ and $\angle GFI$ are supplementary angles since they form a linear - pair.

Step2: Use the supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. Let $m\angle GFI=x$. Then $m\angle GFD + x=180^{\circ}$. Given $m\angle GFD = 129^{\circ}$, we have $x=180^{\circ}-m\angle GFD$.

Step3: Calculate the angle measure

$x = 180 - 129=51^{\circ}$.

Answer:

$51$