*Three Little Kittens*

*Found their Mittens*

*So they shall have some pie.*

*Said one, “The size for me*

*is an arc from A to B*

*and**just shy of 360!”*

* *

Not quite sure what this little kitten was going on about?

Well, the **central angle** is one way we can use to measure circles.

As the name suggests, it is an *angle *with the *vertex *at *circle’s center*. Like this:

Here, we can see that the vertex is the center of the circle, with points A and B on the outer edge. Each side of angle ∠AOB is a **radius**, which means that it is half of the diameter.

The outer edge of the circle between points A and B—the kitten’s pie crust—is an** arc**. The **arc length **is the measurement between A and B along the curve.

Okay, now that we know the terms cold, let’s set up some relationships.

We can make up some ratios. The arc length from AB is a *portion* of the entire circumference. There is **a direct ratio** between the circumference of a circle and its measurement of degrees. The A circle has 360°. The central arc is a portion of that.

Let’s say we know the arc length was 25π and the circumference was 166π. We can calculate the **central angle** easily!

What if we only knew the length of one side of an angle and the arc length?

This is a bit more challenging, but it’s just an extra step.

Let’s recap with our original angle & circle:

Say OA was 6 feet. Arc length is 1.4π

We can calculate the circumference of the circle: *Circumference = Diameter x π*

The* radius* is *half *the diameter, and we know that AO is a radius because it extends from the center of the circle at point O and reaches the outer edge at point A.

*Circumference = Diameter x π* = *2(radius) x π Circumference = 2(6 feet) x π *

*Circumference = 12π*

Great job! Now, we can plug in the numbers into our original formula!

Yep, pretty small angle, all right. Let’s hope that’s not the one our kitty ended up with! Stay tuned to keep learning on online tutoring platform StudyGate.