Question

look at this diagram: 1 if df and gi are parallel lines and m∠feh = 42°, what is m∠deh?

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°. $\angle FEI$ and $\angle DEH$ form a linear pair.

Step2: Set up the equation

Let $m\angle DEH=x$. Since $\angle FEI = 42^{\circ}$ and $\angle FEI+\angle DEH = 180^{\circ}$, we have the equation $42^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

Subtract 42° from both sides of the equation: $x=180^{\circ}- 42^{\circ}$.
$x = 138^{\circ}$

Answer:

$138$