The measure of a central angle tells united state something around its intercepted arc: just how "much the a circle" that arc is. The measure (sometimes called the degree measure) of one arc is same to the measure up of the main angle the intercepts that arc.

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In the number above, both ∠AOB and also arc AB have measures that 90°. Both ∠COE and also arc CDE have actually measures of 180°.

Every arc drops into exactly one the the complying with categories, depending upon its measure.

1. An arc with measure less 보다 180° is a minor arc.2. An arc with measure greater than 180° is a major arc.3. An arc through measure equal to 180° is a semicircle.

Note the a significant arc"s buddy is constantly a boy arc, and vice versa. A semicircle"s friend is constantly a semicircle. They"re basically twins, choose Lindsay Lohan and…uh…Lindsay Lohan.

Sample Problem

An arc has actually a measure of 73°. Is its girlfriend a minor arc, a major arc, or a semicircle arc? What is that is measure?

Since 73° is less than 180°, we recognize that the an initial arc is a boy one. Since the girlfriend of a minor arc is constantly a major arc, we recognize right off the bat that our arc is major. We can find its measure up by subtracting our initial arc indigenous the complete measure of the circle. That provides us 360° – 73° = 287°. Ours arc has a measure up of 287°, much bigger than 180° and also definitely major.

In addition to that measure, arcs have another property dubbed arc length. The length of one arc is the street a an insect would need to crawl native one endpoint of the arc to the other, while remaining on the circle the whole time.

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It"s important to remember that arc length and also arc measure room NOT the same.

If you"re ever unsure whether you"re handling arc length or arc measure, check the units. Arc measure is practically always given in systems of degrees. Arc length, on the various other hand, is a length, and also so it might be provided in units of meters, feet, inches, kilometers, or unhelpfully, "units," yet certainly not degrees. (Don"t be afraid of units. They"re there to assist you.)

It"s pretty necessary to be able to tell once two things room different and when they"re the same. It"s a an excellent skill come have, regardless of exactly how you feel about circles, geometry, or Sesame Street.