How many 45-degree angles does it
take to make a full turn?
First, we need to think about what
a full turn would be. A full turn measures 360
degrees. One way to solve this is setting up
a ratio of the part to the whole. We have a 45-degree angle, and a
whole turn is 360 degrees. If we do some simplification here,
if we divide the numerator by 45, we get one. And if we divide the denominator by
45, we get eight. That means we’re saying a 45-degree
angle is one-eighth of a whole turn.
If we wanted to visualize that, we
could use a circle to represent a full rotation divided in half and half again. Now we have fourths. We have quarter turns. If we divide that in half again,
we’ll have eighths. A 45-degree turn is one-eighth. The question is asking, how many of
those angles would it take to make a full turn? You would have to do that 45-degree
angle eight times to make it back to where you started. And so we can say that it takes
eight 45-degree angles to make a full turn.