Measuring angles with a circular protractor | Math | 4th grade | Khan Academy

Measure the angle in degrees. So here we have this blue angle that we want to measure in degrees, and it's sitting on top of this circle. That circle is actually a protractor. Sometimes we see, and maybe what you're used to seeing, is protractors that are more semicircle shaped, something like this.

Those semicircle protractors measure from 0 to 180°, which is good, but a circle is even better. A full circle is better because an angle can measure up to 360°. So, a full circle allows us to measure an angle of any size instead of only an angle up to 180°. Now, the way we're going to measure this angle is the same way we would on a semicircle protractor.

The first thing we want to do is make sure one of our rays lines up to zero. So here's one of our rays, and it's lining up to zero on the protractor. So that's nice; it's already lined up for us. Then we're going to measure the opening all the way to the other ray, to right here.

So, if our angle only measured and opened up this far, it would be a 10° angle. If, let's say, it opened here, it would be a 50° angle. But our angle measures all the way to here, to the 160°. So, 160° is the measure of our angle. And again, when you measure on a circle protractor or any protractor for that matter, you're going to line one ray up to the zero and then measure the opening till you get to the other ray, which in this case opened up to 160°.