The angles A, B and C of a cyclic quadrilateral ABCD are in the ratio 1 : 2 : 5…

Step 1. One part. $\angle A + \angle C = 180^\circ$ is $6$ parts, so one part is $30^\circ$.

Step 2. Three angles. $\angle A = 30^\circ$, $\angle B = 60^\circ$, $\angle C = 150^\circ$.

Step 3. The fourth angle. $\angle D = 180^\circ - \angle B = 120^\circ$.

Step 4. Check. $30 + 60 + 150 + 120 = 360$.