Question

if GI bisects angle FGH, find angle HGI

Answer 1

Simply set the two expressions equal since it's a bisector.

4x - 29 = 2x - 3

2x = 26 

x = 13. Then plug in to find HGI

2*13-3 = 23 degrees.

Answer 2

If GI bisects ∠FGH, then m∠FGI = m∠HGI
4x - 29 = 2x - 3
4x - 2x = -3 + 29
2x = 26
x = 26/2
x = 13

 m∠HGI = 2x - 3
              = 2*13 - 3
              = 26 - 3
              = 23°