In the diagram, ray gh bisects < fgi. a. solve for x and find < fgh. b. find m< hgic. find m < fgia. x= (simplify your answer)

A bisector divides a line, shape, or angle into two equal halves. The results of the computations are:

Since GH is the bisector of

This means that:

Where:

becomes

Collect like terms

Hence, the value of x is 18

Recall that:

Hence, the value of is 32

Recall that:

So:

Hence, the value of is 32

because

Hence, the value of is 64

Read more about angle bisectors at:

link

Part a.

An angle bisector divides the angle into two congruent angles.

m<FGH = m<HGI

2x - 4 = 3x - 22

Subtract 2x from both sides. Add 22 to both sides.

18 = x

x = 18

Now that we know x = 18,

m<FGH = 2x - 4 = 2(18) - 4 = 36 - 4 = 32

m<FGH = 32

Part b.

m<HGI = 3x - 22 = 3(18) - 22 = 54 - 22 = 32

m<HGI = 32

Part c.

m<FGI = m<FGH + m<HGI = 32 + 32 = 64

m<FGI = 64