Answer:
Option B is correct.
the measure of angle HGI is 21°
Step-by-step explanation:
By Angle bisector definition:
A line that bisects the angle into equal angle
From the given figure, we have;
[tex]\angle FGH = (2x+1)^{\circ}[/tex] and [tex]\angle HGI = (3x-9)^{\circ}[/tex]
it is given that: GH bisects ∠FGI.
then by definition:
[tex]\angle FGH = \angle HGI[/tex]
Substitute the given values we have;
[tex]2x+1 = 3x -9[/tex]
Add 9 to both sides we get;
[tex]2x+10= 3x[/tex]
Subtract 2x from both sides we get;
[tex]10= x[/tex]
or
[tex]x= 10[/tex]
then;
[tex]\angle HGI = 3x-9 = 3(10)-9 = 30-9 = 21^{\circ}[/tex]
Therefore, the measure of angle HGI is 21°
