Question

m∠efg = m∠feh because they are alternate interior angles. m∠fge = m∠gei because they are alternate interior angles. m∠feh + x° + m∠gei = 180° because the three angles form a straight line. so the value of x must be

Explanation:

Step1: Identify equal - angle relationships

Since $\angle EFG$ and $\angle FEH$ are alternate - interior angles, $m\angle EFG=m\angle FEH = 41^{\circ}$. Also, $\angle FGE$ and $\angle GEI$ are alternate - interior angles.

Step2: Use the straight - line angle property

We know that $m\angle FEH+x^{\circ}+m\angle GEI = 180^{\circ}$. Substituting $m\angle FEH = 41^{\circ}$ into the equation, and assuming $m\angle GEI = 41^{\circ}$ (from the alternate - interior angle relationship), we get $41^{\circ}+x^{\circ}+41^{\circ}=180^{\circ}$.

Step3: Solve for $x$

First, simplify the left - hand side of the equation: $82^{\circ}+x^{\circ}=180^{\circ}$. Then, subtract $82^{\circ}$ from both sides: $x^{\circ}=180^{\circ}-82^{\circ}=98^{\circ}$.

Answer:

$98$