The side AB of a cyclic quadrilateral ABCD is extended to E. ∠ ADC = 67°. Find ∠ CBE and ∠ ABC.

Step 1. The exterior angle. $\angle CBE$ equals the interior opposite angle $\angle ADC$. So $\angle CBE = 67^\circ$.

Step 2. The interior angle. $\angle ABC = 180^\circ - 67^\circ = 113^\circ$.

Step 3. Check. $\angle ABC$ and $\angle ADC$ are opposite, and $113 + 67 = 180$.