Question

In the​ diagram, ModifyingAbove GH with right arrow bisects angleFGI.
Angle FGI is formed from angles FGH and HGI. Angle FGH measures 4 x minus 2 degrees. Angle HGI measures 5 x minus 10 degrees.
Upper G
Upper F
Upper H
Upper I
left parenthesis 4 x minus 2 right parenthesis degrees
left parenthesis 5 x minus 10 right parenthesis degrees
a.
Solve for x and find mangleFGH.
b.
Find mangleHGI.
c.
Find mangleFGI.
a. xequals
nothing ​(Simplify your​ answer.)

Answer 1

line GH bisects angle ∠FGI  

∠FGI=3x-3 and ∠HGI=4x-14  

A) solve for x and find m∠FGH  

Since GH bisects ∠FGI, ∠FGI is twice the angle of ∠HGI  

∠FGI = 2*∠HGI  

3x - 3 = 2(4x - 14)  

= 8x - 28  

8x - 3x = 28 - 3 ... transposing 3x and 28 and flipping the equation  

5x = 25  

x = 25/5 ... transposing 5  

= 5  

m∠FGH is equal to ∠HGI  

m∠FGH = 4x - 14  

= 4*5 - 14  

= 6  

B) find ∠HGI  

∠HGI = ∠FGH  

= 6  

C) find ∠FGI  

∠FGI = 2*HGI ... ∠FGI is twice the size of ∠HGI  

= 2*6  

= 12