We have 3 lines and one pair of it, DE and GH are parallel.
We have to find the value of x that satisfy that condition.
If we draw only these lines, we can relate the angles as:
If DE and GH are parallel, then the angle at H, with measure (5x+22), and the angle at D, with measure still to be calculated, are alternate interior angles and therefore have the same measure.
We can calculate the measure of the angle at D using the fact that the sum of the measures of the interior angles of a triangle is equal to 180 degrees.
Then, for triangle DEF, we can write:
[tex]\begin{gathered} m\angle D+m\angle E+m\angle F=180 \\ m\angle D+71+42=180 \\ m\angle D=180-71-42 \\ m\angle D=67 \end{gathered}[/tex]
Now that we know the measure of D, we can write:
[tex]\begin{gathered} m\angle H=m\angle D \\ 5x+22=67 \\ 5x=67-22 \\ 5x=45 \\ x=\frac{45}{5} \\ x=9 \end{gathered}[/tex]
Answer: the value of x is x=9.
