Question

look at this diagram: if $overleftrightarrow{ce}$ and $overleftrightarrow{fh}$ are parallel lines and $mangle hgi = 41^{circ}$, what is $mangle hgd$

Explanation:

Step1: Recall linear - pair property

A linear pair of angles is supplementary, meaning the sum of the angles in a linear pair is 180°. ∠HGI and ∠HGD form a linear pair.
Let \(m\angle HGI = 41^{\circ}\) and \(m\angle HGD=x\). Then \(m\angle HGI + m\angle HGD=180^{\circ}\).

Step2: Solve for \(m\angle HGD\)

We have the equation \(41^{\circ}+x = 180^{\circ}\).
Subtract \(41^{\circ}\) from both sides: \(x=180^{\circ}- 41^{\circ}\).
\(x = 139^{\circ}\).

Answer:

\(139^{\circ}\)