Angles in circles word problem | Math | 4th grade | Khan Academy

If Ariana turns the stove dial 135 degrees to the right, what setting will the dial be on?

So, two very important things up here: first, she's turning the dial 135 degrees, and which way is she turning the dial? She's turning the dial to the right. So here's our dial; it's facing up, this red dial right here, facing up sort of like on a clock. We're going to be turning the dial to the right and how far to the right? 135 degrees.

So this dial will turn until it's reached 135 degrees. So how can we figure out, if we start turning this dial, when to stop when it's reached 135 degrees? Well, one common way would be to use a protractor. We could set up our protractor to measure out 135 degrees, but in this case, we can't do that because we don't have a protractor.

So let's use some other information, some other stuff we know about angles to see if we can solve this. One thing I know, one angle that we see a lot is a 90-degree angle. A 90-degree angle, if we start up at the top like our dial and turn 90 degrees, we're going to end up with an angle like this, an angle where we can put a square in the middle and finish the square. It looks like a square angle, so this is a 90-degree angle.

So coming over to our dial, if we start at the top and we go 90 degrees, so we start here at the top and we go 90 degrees, we'd end up on the low setting. 90 degrees, but we're not going 90; we're going 135, which is more than 90 degrees. So here's one clue: we know we're going farther than the low setting. We don't know how much farther; we're definitely going to go past the low setting.

Another angle I could use to help me is a straight angle, 180 degrees. If 180-degree angle again starts at the top like our knob is currently, like our dial, it will go all the way around until we have a straight angle like this. So again, looking at our knob, if we started at the top and we went around 180 degrees, we would end up facing straight down at medium.

This would be 180 degrees. So where does 135 fall? Well, 135 falls somewhere in between 90 and 180. 90 was not far enough of a turn, and 180 was too far of a turn. So we want something in the middle. And what setting is in the middle of the 90 and the 180? Right here in the middle of them is medium low.

So, turning our stove dial 135 degrees to the right, we'll set our stove to medium low.