Answer:
[tex]x = 4[/tex]
m∠EFH = 21°
m∠EFG = 83°
Step-by-step explanation:
We know that m∠EFH + m∠HFG will be equal to m∠EFG.
Since we know the values of each, we can make the equation:
[tex]5x + 1 + 62 = 18x + 11[/tex]
Let's solve for x by isolating it on one side.
Combine like terms:
[tex]5x + 63 = 18x + 11[/tex]
Subtract 11 from both sides:
[tex]5x + 52 = 18x[/tex]
Subtract 5x from both sides:
[tex]52 = 13x[/tex]
Divide both sides by 13:
[tex]x = 4[/tex]
Now that we know the value of x, we can substitute it inside the formulas for m∠EFH and m∠EFG.
m∠EFH:
[tex]5x+1\\\\5(4)+1\\\\20+1\\\\21[/tex]
m∠EFG:
[tex]18x+11\\\\18(4)+11\\\\72+11\\\\83[/tex]
Hope this helped!
