Question

in the diagram, ray GH bisects <FGI.
a.solve for x and find <FGH.
b. find m<HGI
c. find m <FGI

a. x= (simplify your answer)

Answer 1

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

Answer 2

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

• $x = 18$.
• $\angle FGH = 32$.
• $\angle HGI = 32$.
• $\angle FGI = 64$

Since GH is the bisector of $\angle FGI$

This means that:

$\angle FGH = \angle HGI$

Where:

$\angle FGH = 2x - 4$

$\angle HGI = 3x - 22$

$\angle FGH = \angle HGI$ becomes

$2x - 4 = 3x - 22$

Collect like terms

$3x - 2x = 22 - 4$

$x = 18$

Hence, the value of x is 18

Recall that:

$\angle FGH = 2x - 4$

$\angle FGH = 2 \times 18 - 4$

$\angle FGH = 32$

Hence, the value of $\angle FGH$ is 32

Recall that:

$\angle FGH = \angle HGI$

So:

$\angle HGI = 32$

Hence, the value of $\angle HGI$ is 32

$\angle FGI = 2 \times \angle HGI$ because $\angle FGH = \angle HGI$

$\angle FGI = 2 \times 32$

$\angle FGI = 64$

Hence, the value of $\angle FGI$ is 64

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