Question

if $overleftrightarrow{fh}$ and $overleftrightarrow{ik}$ are parallel lines and $mangle fgj = 119^{circ}$, what is $mangle kjg$?

Explanation:

Step1: Identify angle - relationship

$\angle FGJ$ and $\angle KJG$ are same - side interior angles.

Step2: Apply the property of same - side interior angles

For parallel lines $\overleftrightarrow{FH}$ and $\overleftrightarrow{IK}$, same - side interior angles are supplementary, so $m\angle FGJ+m\angle KJG = 180^{\circ}$.

Step3: Solve for $m\angle KJG$

Given $m\angle FGJ = 119^{\circ}$, then $m\angle KJG=180^{\circ}-m\angle FGJ$. Substitute $m\angle FGJ = 119^{\circ}$ into the equation: $m\angle KJG = 180 - 119=61^{\circ}$.

Answer:

$61$