Given m∠d = 70°, m∠e = 42, and m∠ehg = 68°, prove df is parallel to gh.

we know that

If DF is parallel to GH

then

the measure of the angle EGH must be equal to 70° by corresponding angles

so

Find the measure of the angle EGH

In the triangle EGH

the sum of the internal angles must be equal to 180 degrees

42°+68°+∠EGH=180°

solve for ∠EGH

∠EGH=180-(42+68)

∠EGH=180-110

∠EGH=70°

therefore

The lines DF and GH are parallel