The correct answer is b) 58.
Recognize the angle relationships: Since GK bisects angle FGH, we know that mL FGK = mL KGH.
Set up the equation: We are given that mL FGK = 3v - 4 and mL KGH = 2v + 7. Setting these two expressions equal to each other, we get:
3v - 4 = 2v + 7
Solve for v:
Subtract 2v from both sides:
v - 4 = 7
Add 4 to both sides:
v = 11
Find the measure of angle FGH:
Since mL FGK = 3v - 4 and v = 11, then mL FGK = 3(11) - 4 = 33 - 4 = 29.
Since GK bisects angle FGH, mL FGH = 2 * mL FGK = 2 * 29 = 58.
Therefore, the measure of angle FGH is 58 degrees.
So the correct answer is b) 58.
The question probable may be:
In the figure, GK (with an arrow pointing right) bisects angle FGH.
(L = angle)
if mL FGK = 3v - 4 AND mL KGH = 2v +7
a) 33
b) 58
c) 11
d) 29