Find m∠GEF. This is math homework

Question

In ΔEFG,  EG is extended through point G to point H,  m∠EFG=(2x+1)∘,  m∠FGH=(6x+2)∘,   and m∠GEF=(x+19)∘.   Find m∠GEF.

Answer 1

The measure of an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

<FGH is an exterior angle and <EFG and <GEF are interior angles so:

m<FGH = m<EFG + m<GEF

6x + 2 = 2x + 1 + x + 19

6x + 2 = 3x + 20

3x = 18

x = 6

m<GEF = x + 19 = 6 + 19 = 25

Answer 2

EGH is a straight line, so we know EGF + FGH = 180º

Also, FGH is the external angle so FGH = EFG + GEF

The values are given in the question so the equation becomes

(I removed the units because they are consistent - or you can factor them out)

(6x+2) = (2x + 1) + (x+19)

6x+2 =3x +20

3x =18 so x =6.

What we need is the value of GEF which is x+19 =6+19 =25 º