Question

look at this diagram: if $overleftrightarrow{ce}$ and $overleftrightarrow{fh}$ are parallel lines and $mangle hgi = 136^{circ}$, what is $mangle edg$?

Explanation:

Step1: Identify vertical - angle relationship

$\angle HGI$ and $\angle EDB$ are vertical angles. So, $m\angle EDB=m\angle HGI = 136^{\circ}$

Step2: Use linear - pair property

$\angle EDB$ and $\angle EDG$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So, $m\angle EDB + m\angle EDG=180^{\circ}$

Step3: Solve for $m\angle EDG$

$m\angle EDG=180^{\circ}-m\angle EDB$. Substitute $m\angle EDB = 136^{\circ}$ into the equation: $m\angle EDG=180 - 136=44^{\circ}$

Answer:

$44$