Question

in the figure below, △efg is drawn. the line $overleftrightarrow{hei}$ is drawn such that $overleftrightarrow{hei}paralleloverline{fg}. mangle efg = 41^{circ}$ because they are

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle EFG\), we know two angles and want to find the third. Let \(\angle EFG = 41^{\circ}\), \(\angle FGE=93^{\circ}\), and \(\angle GEF = x\).

Step2: Apply the angle - sum formula

We use the formula \(\angle EFG+\angle FGE+\angle GEF = 180^{\circ}\). Substituting the known values, we get \(41^{\circ}+93^{\circ}+x = 180^{\circ}\).

Step3: Solve for \(x\)

First, add the known angles on the left - hand side: \(41 + 93=134\). So the equation becomes \(134^{\circ}+x = 180^{\circ}\). Then, subtract \(134^{\circ}\) from both sides: \(x=180^{\circ}-134^{\circ}=46^{\circ}\).

Answer:

\(46^{\circ}\)