Question

in the given figure show that A B parallel to CD

Answer 1

it is simple as the sum of consecutive angles is 180 so we can clearly show that AB is parallel to CD

Answer 2

angle IFH = 180 - 100 = 80 degrees (linear pair)
angle IHF = 180 - (80+45) = 180 - 125 = 55 degrees (angle sum property of  a traingle is 180 degrees)
thus, angle EGI and angle IHF are equal (both are 55 degrees)

therefore, since alternate interior angles are equal the two lines AB and CD are parallel with GH transversal