The measure of angle fgh is 116 and gk bisects fgh. what is the measure of fgk?

In the question, it is given that

The measure of angle FGH is 116 and GK bisects FGH.

Since GK bisects angle FGH, it means GK divide angle FGH in two equal parts, angle FGK and angle HGK, and each of them is equal to 58 degree.

So the measurement of angle FGK is 58 degree.