Question

look at this diagram: if $overleftrightarrow{fh}$ and $overleftrightarrow{ik}$ are parallel lines and $mangle kjl = 113^{circ}$, what is $mangle jg$?

Explanation:

Step1: Identify angle - relationship

$\angle KJL$ and $\angle JG F$ are corresponding angles. Since $FH\parallel IK$, corresponding angles are equal. So $m\angle JGF=m\angle KJL = 113^{\circ}$.

Step2: Find $m\angle JG E$

$\angle JGF$ and $\angle JGE$ are a linear - pair. A linear - pair of angles sum to $180^{\circ}$. So $m\angle JGE=180 - m\angle JGF$. Substituting $m\angle JGF = 113^{\circ}$, we get $m\angle JGE=180 - 113=67^{\circ}$.

Step3: Determine $m\angle IJG$

$\angle IJG$ and $\angle JGE$ are alternate interior angles. Since $FH\parallel IK$, alternate interior angles are equal. So $m\angle IJG=m\angle JGE = 67^{\circ}$.

Answer:

$67$