KA-0148Clock geometry: hands, angles, times
4 points, difficulty 2 of 3Level 5–6about 60sWhat is the smaller angle between the hands of a clock at exactly 4 o'clock?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
One hour mark is how many degrees?
2The strategy
The twelve hour marks share 360 degrees between them. Work out what one mark is worth, count the marks between the two hands, and take the smaller of the two ways round.
3The full solution
One mark is 360 divided by 12 = 30 degrees. At 4 o'clock the hands are 4 marks apart, so 4 x 30 = 120 degrees.
Solution
The reliable way
The twelve hour marks divide 360 degrees, so each mark is 30 degrees. At exactly 4 o'clock the minute hand points at 12 and the hour hand at 4, which is 4 marks apart. That is 4 x 30 = 120 degrees. Going the other way round would be 240, so the smaller angle is 120. The transferable idea: fix the 30-degrees-per-mark fact once and every clock question becomes a multiplication - then check which way round the question wants.
The elegant way
Four hours is a third of the clock face, and a third of 360 is 120.
Why this is on the test: The 30-degrees-per-mark fact plus the which-way-round check is the whole of clock geometry at this level.