a How can you divide a 360^(∘) angle into twenty-four congruent angles?
B
b The time zones divide the wheel into congruent sections. How many such sections are between the Tokyo zone and the Anchorage zone?
C
c Which zone is 180^(∘) from the Anchorage zone?
A
a 15^(∘)
B
b 90^(∘)
C
c 3A.M.
Practice makes perfect
a We are given a time zone wheel which can be used to find the time in different locations across the world.
We can see that the time zones divide the wheel into twenty-four congruent sections. Therefore, the arc measures of these sections must be the same. To find the arc measure of one section we have to divide the measure of the circle, 360^(∘), by the number of sections, 24.
We have that the arc measure of one section, which is equivalent to the arc measure between each time zone on the wheel, is 15^(∘).
b We are asked to find the measure of the minor arc from the Tokyo zone to the Anchorage zone. Let's highlight this arc on the time zone wheel.
The minor arc from the Tokyo zone to the Anchorage zone consists of six out of twenty-four congruent sections in which the wheel is divided. Recall that in Part A we determined that the arc measure of one of twenty-four sections is 15^(∘). According to the Arc Addition Postulate, we can write the following.
lThe measure of the minor arc from the Tokyo zone to the Anchorage zone = 6* 15^(∘) =90^(∘)
c We are asked to consider two locations which differ by 180^(∘) on the wheel. It is 3P.M. at one location, and we have to determine what time it is at the other location. Let's consider the given time zone wheel.
The wheel shows that it is 3P.M. at the Anchorage zone. Let's determine which zone on the wheel is 180^(∘) from the Anchorage zone. Since the measure of each minor arc on the wheel is 15^(∘), the zone we are looking for is 180^(∘) 15^(∘)=12 minor arcs from the Anchorage zone.
We can see that the Kuwait City zone and the Anchorage zone differ by 180^(∘), and it is 3A.M. at the Kuwait City zone. Now we will complete the given statement.
If two locations differ by 180^(∘) on the wheel, then it is 3P.M. at one location when it is 3A.M. at the other location.
