Question

look at this diagram: if (overleftrightarrow{fh}) and (overleftrightarrow{ik}) are parallel lines and (mangle ijg = 136^{circ}), what is (mangle hgj?)

Explanation:

Step1: Identify angle - relationship

$\angle IJG$ and $\angle HGF$ are corresponding angles. Since $\overleftrightarrow{FH}\parallel\overleftrightarrow{IK}$, $\angle IJG=\angle HGF = 136^{\circ}$.

Step2: Use linear - pair property

$\angle HGF$ and $\angle HGI$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $\angle HGI = 180^{\circ}-\angle HGF$.

Step3: Calculate $\angle HGI$

$\angle HGI=180 - 136=44^{\circ}$.

Step4: Identify vertical - angle relationship

$\angle HGI$ and $\angle HGJ$ are vertical angles. Vertical angles are equal. So $\angle HGJ=\angle HGI$.

Answer:

$44$