Question

In the​ diagram, GH bisects ∠FGI.

Answer 1

An angle bisector divides the angle into equal halves.

• The value of x is 20
• FGH = HGI = 35
• FGI = 70

From the question, we understand that GH bisects FGI.

This means that:

$< fgh \: = < hgi$

So, we have:

$2x - 5 = 3x - 25$

Collect like terms

$3x - 2x = 25 - 5$

Evaluate like terms

$x = 20$

From the question

$< fgh \: = 2x - 5$

Substitute 20 for x

$< fgh \: = 2 \times 20 - 5$

$< fgh \: = 35$

Recall that:

$< fgh \: = < hgi$

This means that:

$< hgi \: = 35$

The measure of FGI is the sum of both angles.

So, we have:

$< fgi \: = 35 + 35$

$< fgi = 70$

Read more about angle bisectors at:

brainly.com/question/2478436