ABCD is a cyclic trapezium with AB ∥ DC and ∠ DAB = 64°. Find ∠ ADC, ∠ ABC and ∠ BCD.

Step 1. The angle D. $AB \parallel DC$, so $\angle ADC = 180^\circ - 64^\circ = 116^\circ$.

Step 2. The angle C. It is opposite to $\angle A$, so $\angle BCD = 180^\circ - 64^\circ = 116^\circ$.

Step 3. The angle B. It is opposite to $\angle D$, so $\angle ABC = 180^\circ - 116^\circ = 64^\circ$.

Step 4. Notice. $\angle A = \angle B$ and $\angle C = \angle D$. The trapezium is isosceles.