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Current time:0:00Total duration:6:36
CCSS.Math:

Video transcript

so I have some example questions here from Khan Academy on arc measure and like always I encourage you to pause the video after you see each of these questions and try to solve them before I do so this first question says what is the arc measure in degrees of Arc AC on circle P below so this is point a that is Point C and when they're talking about arc AC since they only have two letters here we can assume it's going to be the minor arc and we talked about the minor arc there's two potential arcs that connect point a and Point C there's a one here on the left and then there's the one on there is the one on the right and since C isn't exactly isn't exactly straight down from a it's a little bit to the right the shorter arc the arc with a smaller length or the minor arc is going to be this one that I'm depicting here right on the right so what is this arc measure going to be well the measure of this arc is going to be exactly the same thing as in degrees as the measure of the central angle that intercepts the arc so that's central angle let me do it in a different color I'll do it in this blue color that central angle is angle C P a angles CPA and the measure of that central angle is going to be 70 degrees plus 104 degrees it's going to be this whole thing right over there so it's going to be 174 degrees 174 degrees that's the arc measure in degrees of Arc AC let's keep doing these so let me do another one so this next one asks us in the figure below in the figure below segment ad so this is point a this is point D so segment ad is this one right over here let me see if I can draw that that's a D right over there ad and C are diameters of the circle so let me draw C e so C E is we're going to connect Point C and E these are diameters so let me so they go straight whoops I'm using the wrong tool let me so those are somehow I should i alright so those are diet whoops how did that happen so let me somehow my pin got really big alright that me almost there okay so see II there you go so those are both diameters of the circle P what is the arc measure of a B of arc a B and degrees so arc a B once again there's two potential arcs that connect point a and B there's the minor arc consist this only has two letters we'll assume it's the mine arc it's going to be this one over here there's a major arc but to denote the major arc they would have said something like a EB or ADB or arc ACB to make us go this kind of the this long way around but this is arc a B so we in order to find the arc measure we just really have to find the measure of the central angle this is a central angle that intercepts that arc or you could even say it defines that arc in some way so how can we figure out this angle this one's a little bit trickier well the key to the key here is to realize that this is 93 degree angle it is vertical to this whole angle right over here and we know from geometry which we're still learning as we do this example problem that vertical angles are going to have the same measure so if this one on this one is 93 degrees in this entire blue one right over here is also going to be let me write it this is also going to be 93 degrees so 93 degrees that's going to be made up of this red angle that we care about and the 38 degrees so this red one which is which is the measure of the central angle it's also the arc measure of Arc a B is going to be 93 minus 93 degrees minus 38 degrees so what is that going to be let's say 93 I can write degrees there - 38 degrees that is going to be equal to C if it was 93 minus 40 it would be it would be 53 it's going to be two more it's going to be 55 degrees 55 degrees and we are done this angle right over here is 55 degrees if you were to add this angle measure plus 38 degrees you'd get 93 degrees and that has the same measure because it's vertical with this angle right over here with angle D P e alright let's do one more of these so we have in the figure below and it doesn't quite fit on the page but we'll scroll down in a second a B is the diameter of circle P is the diameter of circle P all right so a B is a diameter let me label that so a B is a diameter so going straight across straight across the circle what is the arc measure of a B C in degrees so a B C so they're making us go the long way around this is a major arc they're talking about let me draw it arc a what is the arc measure of Arc ABC so we're going the long way around so it's a major arc so what is that going to be well it's going to be in degrees the same measure as the angle as the central angle that intercepts it so it's going to be the same thing as this central angle right over here well what is that central angle going to be well since we know that this is a diameter since a B is a diameter we know we know that this part of it this part of it is going to be 180 degrees we're going halfway around the circle 180 degrees and so if we want to look at this whole angle the angle that intercepts the major arc ABC it's going to be the 180 degrees plus 69 degrees so we're going to have 180 degrees plus 69 degrees which is equal to what is that 249 249 degrees that's the arc measure of this major arc ABC