Answer:
as i see from the picture, this lecture mainly taught you relationship of the angles in a specific condition
such as
corresponding angles, AB//CD ,
alternate angles, AB//CD ,
interior angles, AB//CD
In my figure, a+b is always equal to 180degree if the X line is straight
a+b=180
imagine there is Y line which is parallel to the X line
c+d=180
a=c, b=d because y line and x line is parallel (corresponding angles,X//Y)
then b+a=180, substitute c as a, b+c=180(interior angles, X//Y)