a How many degrees does the hour hand move in one hour?
B
b How many "hours" are there between the hands?
C
c A straight angle measures 180^(∘).
A
a 60^(∘)
B
b 150^(∘)
C
cExample Solution: 6:00
Practice makes perfect
a Let's draw the clock when it's 10:00 and mark the acute angle.
At this time, the minute hand points up, and the hour hand points straight at ten. How can we find the measure of that angle? Because the motion of the hands of a clock is a full circle, there is a 360^(∘) revolution every 12 hours. This means that, between each hour on the clock, there are 360^(∘)12=30^(∘).
The angle between the ten and the twelve is, therefore, 30^(∘) twice.
2* 30^(∘) = 60^(∘)
b This time, let's draw the clock when it's 5:00.
The hour hand points to the five and the minute hand to the twelve. From Part A, we know that the hour hand moves 30^(∘) every hour. Therefore, the angle between the minute and hour hands is 30^(∘) five times.
5*30^(∘) = 150^(∘)
c A straight angle measures 180^(∘). If we keep the minute hand at twelve, the hour hand should be pointing in the exact opposite direction.
This means that when the clock reads 6:00, the angle between the minute and hour hands is straight. Note that this is only one of many examples of a straight angle on a clock.
