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Stephan Branczyk · Answer 1 · 2023-02-22T12:55:00+0000

Given:

The lines l and m are parallel lines and x=40 degrees.

To find the angle:

$\angle\text{DEF}$

We know that alternate angles are equal.

So that,

$\begin{gathered} \angle EDG=x \\ =40^(\circ) \end{gathered}$

And then, using the angle sum property of a triangle,

$\begin{gathered} \angle EDG+\angle DFE+\angle DEF=180^(\circ) \\ 40^(\circ)+40^(\circ)+\angle DEF=180^(\circ) \\ \angle DEF=180^(\circ)-40^(\circ)-40^(\circ) \\ \angle DEF=100^(\circ) \end{gathered}$

Thus, the measure of angle DEF is 100 degrees.

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