Question

angle EFG and angle GFH are a linear pair, m angle GFH= 2n+38 and m angle GFH=2n+38. what are m angle EFG and m angle GFH

Answer 1

`m<EFG=92`

`m<GFH=86`

Explanation:

angle EFG and angle GFH are a linear pair

m<EFG +m<GFH = 180 degree because it is linear pair

m<EFG= 3n+22 and m<GFH=2n+38

m<EFG +m<GFH = 180

`3n+22+2n+38=180`

Combine like terms

`5n+60=180`

Subtract 60 from both sides

`5n=120`

Divide both sides by 5

n=24

`m<EFG= 3n+22 =3(24)+22=92`

`m<GFH=2n+38 =2(24)+38=86`

Answer 2

Part 1) m∠EFG=94°

Part 2) m∠GFH=86°

Explanation:

we know that

m∠EFG+m∠GFH=180° -----> by linear pair (given problem)

we have

m∠EFG=3n+22

m∠GFH=2n+38

substitute the values

(3n+22)°+(2n+38)°=180°

Solve for n

(5n+60)=180

5n=180-60

5n=120

n=24

Find the measure of angle EFG

m∠EFG=3n+22

substitute the value of n

m∠EFG=3(24)+22=94°

Find the measure of angle GFH

m∠GFH=2n+38

substitute the value of n

m∠GFH=2(24)+38=86°