a) The measure of vertical angles are the same, they are congruent angles.
b) This occurs because if you choose one of the four angles, the two adjacent angles to this angle will be supplementary to the first angle, so they need to have the same measure.
For example, if angle GEF is equal 120°, the angle FEM is supplementary to GEF, and the angle GEH is also supplementary to GEF, and the supplementary angle can only have one value, therefore the angles FEM and GEH are congruent.
