IMC 2006 Q11
11. What is the obtuse angle between the hands of a clock at 6 minutes past 8 o'clock?
- A 123°
- B 126°
- C 153°
- D 156°
- E 159°
Intermediate Mathematical Challenge 2006, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 153°
At 8 o'clock, the obtuse angle between the hands of the clock is 120°. In the following six minutes, the minute hand turns though an angle of 36° whilst the hour hand turns through an angle of 3° in the same direction (clockwise!). So the obtuse angle between the hands increases by 33°.
Solution © UK Mathematics Trust, from the IMC 2006 solutions.