Show that AB is not parallel to CD.

Question has two figures: a trapezium with angles 60, 2x, 3x,x and two lines AB and CD with a line across them forming conjugate angle sets with the two labelled angles 120 and x not part of the same pair.

1. Establish the conditions under which AB is parallel to CD. Rule = conjugate angles, opposite angles are the same and sum of angles (one from each pair) is 180. So if AB is parallel to CD, x= 180-120=60.
2. Find value of x in trapezium. Rule = total angles in a trapezium is 360. Sum of angles = 60+2x+3x+x= 360. --> 60 + 6x= 360 --> 6x=300 --> x = 50.
3. Compare result to condition set in step 1. x does not = 60 so AB is not parallel to CD.