Question

in this figure AB || CD and EF is a transversal find the value of x in terms of q°​

Answer 1

Angle GHD= Angle AGH = q { alternate interior angles}

Angle GHD + Angle DHF = 180. { linear pair}
q + x= 180
x = 180-q

Answer 2

Answer: ∠GHD = q (because alternate interior angles are equal)

                   now ∠x + ∠GHD =180°

                     x= 180° - ∠GHD   = 180° - q (as q = ∠GHD)

alternate method

                    ∠EGA = 180° - q

                     now ∠EGA = ∠x as the are alternate exterior angles

                   ∠x = 180° - q

alternate method

                    ∠BGH = 180°- q

                      now ∠BGH = x   ( as they are corresponding angles, and corresponding angles are equal)

                            ⇒ ∠x = 180°- q

hope this helps you