Question

What is the size of the reflex angle between the hands of a clock at 4 O'clock, 3 o'clock, and 10 o'clock?​

Answer 1

At 3:00 the minute hand is at 12 and the hour hand at 3. So the two hands form a reflex angle = 360–3*30 = 360–90 = 270 deg. Alternatively, the reflex angle = (12–3)*30 = 9*30 = 270 deg.

At 5:00 the minute hand is at 12 and the hour hand at 5. So the two hands form a reflex angle = 360–5*30 = 360–150 = 210 deg. Alternatively, the reflex angle = (12–5)*30 = 7*30 = 210 deg.

At 8:00 the minute hand is at 12 and the hour hand at 8. So the two hands form a reflex angle = 8*30 = 240 deg.