Question Video: Using Angle Measures to Find the Number of Partial Turns in a Full Turn Mathematics

How many 45° angles does it take to make a full turn?


Video Transcript

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.

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