Measure of an Arc: Process & Practice

Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

The measure of an arc can be solved by determining the degree of the angle that intercepts an arc. Learn about the process of measuring an arc, major vs. minor arcs, and real-world practice arc problems. Updated: 09/28/2021

What Is an Arc?

Depending on where you live, you might encounter different kinds of arcs. If you have a neighbor named Noah, you might be familiar with this kind of ark. That's 'ark' with a 'k.' By the way, if Noah is your neighbor, you might want to get some flood insurance. If you live in an Indiana Jones movie, you might be familiar with this kind of ark. This is also 'ark' with a 'k.' Also, it has a tendency to kill everyone near it, especially Nazis, so you might want to avert your eyes.

And then there's 'arc' with a 'c.' This is the arc of circles. 'Circle' begins with 'c,' so that makes sense. An arc, in terms of a circle, is a part of a circle's circumference, or edge. If you prefer your circles in pie form, then an arc is the flaky crust keeping in that delicious pumpkin filling on your slice. I know I like my vegetables in pie form, and I love me some pumpkin pie.

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  • 0:06 What is an Arc?
  • 0:58 Major and Minor Arcs
  • 1:57 Measure of an Arc
  • 3:14 Practice with Arc Measurements
  • 4:13 Lesson Summary
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Major and Minor Arcs

If you're like me, then when you cut a slice of pie, you have to stop and think about the two arcs you just created. Your knife makes two points on the circle. Let's call them A and B. If we focus on the normal slice, we call that the minor arc, or the shorter arc joining two points on a circle's edge. That's arc AB.

And then there's the major arc, or the longer arc joining two points on a circle's edge. You could think of this in terms of major and minor leagues in baseball. Major leagues are the big time, so major arc is the bigger one.

But wait. Do we also call that arc AB? We can. But that could mean the major or minor arc. So sometimes we just say major arc AB. Or we add a point like this. Then the major arc is arc AQB. As for the pie, you could totally take that gigantic major arc slice. But you resist, right?

Major Arc
Major Arc

Measure of an Arc

Now maybe you're comparing slices of this key lime pie and this key lime tart. No matter what, this counts as a fruit, right? Anyway, this is where we differentiate between an arc's measure and its length. The measure of an arc is the degree measurement of the angle that intercepts the arc. The measure of an arc is written as mAB.

Notice that I said it's the degree measurement. That's important. And it's different than an arc's length, which is the distance along the circumference of the arc. Look at our comparable pie and tart slices. The length of the arc on the pie slice is a few inches. On the tart? Barely an inch. But the measure of these arcs is the same. It's based on the degree of this angle, the tip of our piece.

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