Question

4. FH bisects ∠GFI, m∠EFG = 4y + 8 and m∠HFI = 2y + 6. Find m∠EFH.

please help me solve this

Answer 1

Angle EFH is 134 degrees.

Answer 2

m∠EFH=134

Explanation:

FH bisects ∠GFI

So m<GFH=m<HFI

m∠EFG = 4y + 8 and m∠HFI = 2y + 6

m<GFH=2y+6

`m<EFG+m<GF+m<HFI= 180` because its a linear pair

`4y+8+2y+6+2y+6=180`

combine like terms and solve for y

`8y+20=180`

Subtract 20 from both sides

`8y=160`

Divide both sides by 8

y=20

m∠EFH=m<EFG+m<GFH

m∠EFH=
`4y+8+2y+6=6y+14=6(20)+14=134`