Answer:
50 degrees.
Step-by-step explanation:
Angle FGE = [tex]180-(7x+18)[/tex] because angles on a straight line add up to 180 degrees.
Angle EFG = [tex]180-38-(180-(7x+18))=6x-10[/tex] (Angles in a triangle add up to 180)
[tex]180-38-\left(-7x+162\right)=6x-10[/tex]
[tex]180-38+7x-162=6x-10[/tex]
[tex]7x-20=6x-10[/tex]
Add 20 to both sides:
[tex]7x-20+20=6x-10+20[/tex]
[tex]7x=6x+10[/tex]
Subtract 6x from both sides:
[tex]7x-6x=6x+10-6x[/tex]
[tex]x=10[/tex]
Angle [tex]EFG=6x-10=6(10)-10=60-10=50[/tex]
