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In the​ diagram, GH bisects ∠FGI.
Angle FGI is formed from angles FGH and HGI. Angle FGH measures 2 x minus 5 degrees. Angle HGI measures 3 x minus 25 degrees.
G
F
H
I
(2x−5)°
(3x−25)°
a.
Solve for x and find m∠FGH.
b.
Find m∠HGI.
c.
Find m∠FGI.

In the diagram GH bisects FGIAngle FGI is formed from angles FGH and HGI Angle FGH measures 2 x minus 5 degrees Angle HGI measures 3 x minus 25 degreesGFHI2x53x class=

Respuesta :

MrRoyal

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:

[tex] < fgh \: = < hgi[/tex]

So, we have:

[tex]2x - 5 = 3x - 25[/tex]

Collect like terms

[tex]3x - 2x = 25 - 5[/tex]

Evaluate like terms

[tex]x = 20[/tex]

From the question

[tex] < fgh \: = 2x - 5[/tex]

Substitute 20 for x

[tex] < fgh \: = 2 \times 20 - 5[/tex]

[tex] < fgh \: = 35[/tex]

Recall that:

[tex] < fgh \: = < hgi[/tex]

This means that:

[tex] < hgi \: = 35[/tex]

The measure of FGI is the sum of both angles.

So, we have:

[tex] < fgi \: = 35 + 35[/tex]

[tex] < fgi = 70[/tex]

Read more about angle bisectors at:

https://brainly.com/question/2478436

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