Answer :
Given:
Consider the below figure attached with this question.
∠EFH = (5x + 1)°, ∠HFG = 62°, and ∠EFG = (18x + 11)°
To find:
The measure of ∠EFH.
Solution:
From the figure it is clear that ∠EFG is divide in two parts ∠EFH and ∠HFG. So,
[tex]\angle EFG=\angle EFH+\angle HFG[/tex]
[tex]18x+11=(5x+1)+(62)[/tex]
[tex]18x+11=5x+63[/tex]
Isolate variable terms.
[tex]18x-5x=63-11[/tex]
[tex]13x=52[/tex]
Divide both sides by 13.
[tex]x=\dfrac{52}{13}[/tex]
[tex]x=4[/tex]
The value of x is 4.
[tex]\angle EFH=(5x+1)^\circ[/tex]
[tex]\angle EFH=(5(4)+1)^\circ[/tex]
[tex]\angle EFH=(20+1)^\circ[/tex]
[tex]\angle EFH=21^\circ[/tex]
Therefore, the measure of ∠EFH is 21°.
