## A Circle of Arcs

Angles Measuring angles in degrees. Video transcript We already know that an angle is formed when two rays share a common endpoint. So, for example, let's say that this is one ray right over here, and then this is one another ray right over here, and then they would form an angle. And at this point right over here, their common endpoint is called the vertex of that angle. Now, we also know that not all angles seem the same. For example, this is one angle here, and then we could have another angle that looks something like this. And viewed this way, it looks like this one is much more open.

So I'll say more open.

## Circles, Arcs and Sectors

And this one right over here seems less open. So to avoid having to just say, oh, more open and less open and actually becoming a little bit more exact about it, we'd actually want to measure how open an angle is, or we'd want to have a measure of the angle. Now, the most typical way that angles are measured, there's actually two major ways of that they're measured. The most typical unit is in degrees, but later on in high school, you'll also see the unit of radians being used, especially when you learn trigonometry.

But the degrees convention really comes from a circle. So let's draw ourselves a circle right over here, so that's a circle.

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And the convention is that-- when I say convention, it's just kind of what everyone has been doing. The convention is that you have degrees in a circle. So let me explain that. So if that's the center of the circle, and if we make this ray our starting point or one side of our angle, if you go all the way around the circle, that represents degrees. And the notation is , and then this little superscript circle represents degrees. This could be read as degrees. Now, you might be saying, where did this number come from? And no one knows for sure, but there's hints in history, and there's hints in just the way that the universe works, or at least the Earth's rotation around the sun.

You might recognize or you might already realize that there are days in a non-leap year, in a leap year. And so you can imagine ancient astronomers might have said, well, you know, that's pretty close to And in fact, several ancient calendars, including the Persians and the Mayans, had days in their year. And is also a much neater number than It has many, many more factors. An ellipse will be drawn with the sides touching a rectangular box defined by the starting and stopping points of the drag. To force a circle to be drawn, hold down the Ctrl while dragging the mouse.

Holding the Shift key down while dragging will create an ellipse centered around the starting point.

### Example Questions

Holding down the Alt key while dragging will create an ellipse with the circumference passing through the start and end points of the drag. When an ellipse is selected and the Ellipse Tool is active, the ellipse will have a set of handles small squares and circles that can be used to resize it or convert it to an arc.

The handles are also available if one of other shape Tools or the Node Tool is active. To change the size of the ellipse, drag the handle at the top or left. The Ctrl key can be used to force the ellipse to be a circle.

## How to find the length of an arc - SAT Math

To convert an ellipse into an arc, use the two Arc handles. Initially both handles are on top of each other. And this value is the numerical portion of my answer. Since this value stands for "area", which is a square dimension, I'll want to remember to put "squared" on the units they gave me for the radius. Sometimes, an exercise will give you information, but, like the above, it might not seem like it's the information that you actually need. Don't be afraid to fiddle with the values and the formulas; try to see if you can figure out a back door in to a solution, or some other manipulation that'll give you want you need. It's okay not to know, right at the beginning, how you're going to reach the end. And, if they give you, or ask for, the diameter, remember that the radius is half of the diameter, and the diameter is twice the radius.

They've asked me for the diameter.

The formulas I've learned use the radius. But I can find the radius, and then double it to get the diameter, so that's not a problem. However, they've asked me for a length, given the arc length and the area, each of which uses the radius and the subtended angle. And I have neither of those values.

So what do I do? When I can't think of anything else to do, I plug whatever they've given me into whatever formulas might relate, and I hope something drops out of it that I can use. I can substitute from the second line above into the first line above after some rearrangement , and see if the result helps me at all:.

## Arc of a Circle

I found the value for the radius! I don't have the value for the central angle, but they didn't ask for that, and it turns out that I didn't need it anyway. They asked me for the diameter, which is twice the radius, so my answer including the units! Page 1 Page 2 Page 3. All right reserved.