In the quadrilateral HGFE, the angle `/_ GHF = /_ HFE = 34^@` For the lines HG and EF, HF is a transversal and `/_GHF` and `/_HFE` are alternate interior angles. As they are equal, the lines HG and EF area parallel.
The quadrilateral in the first figure has two parallel lines. This follows from the consecutive interior angles adding up to `100^@ + 80^@ = 180^@`. In the second figure HE and GF are not parallel.