What is the reflex angle between the hour hand and the minute hand at 4:36?

Explanation

1. 01

   Smaller angle $= |30 \times 4 - 5.5 \times 36| = |120 - 198| = 78^\circ$.

2. 02

   The reflex angle is the other side of the dial: $360 - 78 = 282^\circ$.