Answer: [tex]m\angle EFG=62^{\circ},\ m\angle GFH =118^{\circ} .[/tex]
Step-by-step explanation:
We know that a linear pair is pair of angles whose sum is 180°.
Given, ∠ EFG and ∠ GFH are a linear pair
[tex]m\angle EFG= s^2n+22[/tex] and [tex]m\angleGFH = 4n+38[/tex]
By definition of linear pair.
[tex]m\angle EFG+m\angle GFH = 180^{\circ}\\\\\Rightarrow\ 2n+22+4n+38=180\\\\\Rightarrow6n+60=180\\\\\Rightarrow6n=180-60 \\\\\Rightarrow6n=120\\\\\Rightarrow n=20[/tex]
Now,
[tex]m\angle EFG = 2(20)+22=40+22=62^{\circ}\\\\ m\angle GFH = 4(20)+38=80+38=118^{\circ}[/tex]
Hence, [tex]m\angle EFG=62^{\circ},\ m\angle GFH =118^{\circ} .[/tex]
