Arc Length and Arc Measure

Most of you are asking, What is Arc length and what is the Arc measure? Well, first of all you must understand what an arc is. An arc is an angle formed with the center point as a vertices (similar to a Central Angle) which includes the distance between two points on a circle (the Arc Length), and the measure of the angle of the arc (Arc Measure). As seen here:
external image arc_85degrees_CCCCFF.jpg

Finding Arc Length

To find arc length you can use this equation: C x Arc measure(Central Angle)/360=Arc Length. Such as this arc:
external image circle-arc-length.gif
You see that 15 number on that segment? That is a radius, in which, that number times two. Which equals 30, then you take 30 times pie to find the circumference. Then you take 94.25 times the arc measure (60 degrees) divided by 360 degrees. The arc length for this arc is 15.7. What about the other arc? Well, just take 360 - 15.7 and you will get the other arc length. All arc lengths added up equal to 360, as well as the Arc measures.
Arc Length Calculator

Finding Arc Measure

To find the Arc Measure you will need to use the Arc length equation. Instead the Arc measure is a variable. Like this: Arc Length= X/360 x Circumference. So, lets say your arc measure is 75 degrees:
external image circle-arc-length.gif
So your equation would look like this so far: 75= X/360 x Circumference. Now, let's say your circumference is 40. Now your equation should look like this: 75= X/360 x 40. Now we need to use substitution to get X all by itself. First you times the right side of the equation by 360: 75(360)= X x 40. Then you must times 75 by 360: 2700, then you divide X times 40 by 40 on both sides: 2700/40= (X x 40)/40. After you have done that you should get X= 67.5.