Question

look at this diagram: if (overline{df}) and (overline{gi}) are parallel lines and (mangle fec = 138^{circ}), what is (mangle feh)?

Explanation:

Step1: Identify angle - pair relationship

$\angle FEC$ and $\angle FEH$ are a linear - pair of angles.

Step2: Recall linear - pair property

The sum of the measures of a linear pair of angles is $180^{\circ}$. So, $m\angle FEC + m\angle FEH=180^{\circ}$.

Step3: Solve for $m\angle FEH$

Given $m\angle FEC = 138^{\circ}$, we substitute into the equation: $m\angle FEH=180^{\circ}-m\angle FEC$.
$m\angle FEH = 180 - 138=42^{\circ}$.

Answer:

$42^{\circ}$