Video Gallery

10.5 Notes AP

Go to Video Gallery Added Apr 14, 2016 •

Copy this URL:
Embed code:	<iframe class="edlio-embed-player" type="text/html" width="640" height="360" src="//hs.cantonisd.net/apps/embed/?v=110308" frameborder="0" allowfullscreen></iframe> Change dimensions

Go HD

Show Transcript

10.5 is about the other angle relationships in a circle besides the two that we've already learned now the two that we've already learned are central angles and inscribed angles and if you'll remember a central angle the vertex is on the center and it makes a minor Arc and then it also makes the major arc but this is your central angle and then an inscribed angle the vertex is on the circle and it makes an inner SEPTA dark that's on the inside of the angle in this is your angle know if you'll remember a central angle equals the arc measure so these who were the same The Arc measure and the angle measure have to be the same and inscribed the inscribed angle was half of its Arc measure now what the vertex is not on the center and not on the circle so it's somewhere else either outside or inside the circle and that's what we're going to look at today so ceram 10.14 is the first one that we have and it says if a tangent and a chord intersect at a point on the circle then I'll look here's at and here's chord AB they intersect their vertex is on the circle then the measure of each angle formed is one half the measure of the intercepted Arc this one the vertex is on the circle it has the exact same rule as your inscribed angle if the vertex is on the circle then the measure of that angle is half of its Arc so if you'll look right here then go equals half of the intercepted Arc so one on this site is half of Arc ATB so ATV this Arc so it half of that one okay so this Ark and Goins half of that okay and angle 2 is half of just art a be so starting at 8 and going to be that angle is half of that Arc know if you look at their example that we have right here using that if this angle is 80 degrees then the arc that's with it now the angle is half so the arc is 160 degrees more on this side they give us the arc 200 so the angle is half of that so this angle is 100 degrees now if you will notice this Cohasset equal 360 will 200 160 equal 360 and then you'll notice these two angles make a straight line and they have to equal 180 and they do all right now let's go to the next page  when two lines intersect Circle there are three places the lines can intersect they can intersect on the which makes that an inscribed angle they can intersect inside the circle it can be the sinner but it doesn't have to be or they can intersect outside the circle and it can be anywhere outside of the circle now this situation we already know this angle one makes this Arc and the Google  equals half of the Ark now here's our to new situations let's say we have to fund this single well first off we know that the angle is congruent to that angle because they are vertical angles and those two angles make this Arc and this and there's going to be a formula that uses both of them sharks and then you'll notice on this outside angle for need to find that one it has this arkancide in this Ark inside of it now it's going to be real similar to this you're going to take half but in this one you're going to add and then take half and in this one you're going to subtract and take half and that's all the angles that are possible within circles so let's look at their and .15 if they intersect on the inside the angle is one half the sum meaning the addition of the intercepted arcs angle 1 and 2 here are vertical angles so we know they have to have the same measurement angle 2 does art be an angle one has Arc a no angle one is half of Arkay plus art be so you're going to add this Arc and this Arc together then take love it and that will give you angle 1 and angle 2 know you could find these two angles if you know those two arcs you would add those together in / 2 or if you know one or two these are a linear pair and you can find those two angles so let's look at our example down here using that if I want to fun single right here when a bad ankle one-hit makes this Ark  and that Ark so all you have to do is 1/2 of 35 + 80 which is 35 + 80 is 115 take half of 115 and you get 57.5 degrees this single right here is 57.5 degrees number make it a little bigger so I can write it on there so that equals 57 5 degrees this angle 57.5 degrees and if we subtracted from 180 we would find out that these two angles are 120 2.5 Greece  all right let's look at the next one there in 10.16 if they intersect outside the circle the angle is one half the difference you subtract of the intercepted Arts Soffer angle one you have Arc B & R hey so what you do and you're always going to do the bigger one minus the smaller one which is right here angle 1 equals 1/2 RK Morris art B and then you take half of that okay now in this situation outside we're going to have three different situation will have two tangents can an attention or 2 secrets this is 2 secrets that's what it's going to look like now if we have a secant right here in a tan those are going to intersect write the Arts are going to touch each other actually so it will be this our minus this Arc to get that angle  so this would be your a in this would be your okay and if you have two tangent lines here there's a special thing about that  it crosses where in there you're going to have this Ark from that point to that point - this art from that point to that point and that's going to give you a one so this is your a in this is your beat now one thing to look here if I add those two hearts together they make the full circle so we know that these are going to add up to 3 so they may just give you one Ark and you can subtract from 360 to find the other Arc right let's look at our example now we have this one we want find the angle right here and that makes this Arc  and it makes this Arc so this is a secant and a tangent and then meet right there so 1/2 the Big Arc is 120 - the smaller I can 68 and if we should back those were going to get 52  and half of 52 is 26 degrees so this angle right where is 26 degrees you can find that one is 26 subtract from 180 and you could say this is 154 in this is 154 if you need to we're just asking for that angle at the moment at these two at the bottom okay we have this so it intersects on the outside no remember if it you're sexy inside you add the Arts and divided by 2 if it intersects on the outside you at a you subtract the Arts and divided by 2 what is this situation that is where the vertex is on the circle and if the vertex is on the circle not inside or outside it is for the intercepted Arc so let's go back to this problem so we know we have this sort IS 250  and we need to what this Arc but we don't know what that Arc is but since that me to makes a full circle to find that Arc you would do 360° minus 250 degrees and you get 110 degrees so this Arc right here is 110 now you can attract and take half so half of 250 - 110 250 - 110 is 140 half of that is 70° so this single right here is 70 degrees so that means it's half of the arc so if this Arc right here is 220 half of that is 110 degrees and then you can find this Arc in this angle you can subtract from 360 to find this our car you can subtract from 180 to find that angle if I should track from 180 I know that this single has to be 70 and then this Ark is double that 140 140 and 220 make 361 10 and 70 make 1 okay an exercise 6 or 8 find the value of x let's look at number 6 where is are vertex they cross right there so they're on the inside now they give us this angle to software but we don't know anything about the Arts that it makes but we do know the arcs that these two angles so fun fun this angle then these two have to equal 180 or you can subtract from 180 and find the single so what we would do is the first thing we would do is we would want to find this angle right here so we're going to do 1/2 of 97 MI 35/2 of 97 - 35 is 132 sorry and does 132 is 66 degrees now we know this angle is 66 degrees so two ways you can do this you can say 66 plus this equals 1 or you can go ahead and subtract from 180 the 166 and you'll get that this angle is 114 so we know that this has to equal 114 degrees so if we do that way we can just do 5 x + 14 equals 114 subtract the 14 5x equals 100 / 5 + x equals 20 turn number 7 your vertex is on the outside and it gives you the angle and you have to solve for one of the Arts we know this Arc - this Ark divided by 2 equals this angle set that equation up just like we set it we know that x - 72 what about two equals 38 degrees you could do one half of x minus 72 equals 38 degrees this is the same thing x 1/2 or dividing by to whichever way you like you can set up you can distribute this one half and then solve for x you can multiply both sides by two to get rid of the 1/2 first over here if you set it up like this think about this being over one and cross multiplying so there's lots of ways you can solve this algebraically now if we do it this way x - 72 times 1 is one and then this cross the two times the 38 you get 76 so now all you have to do is add the 7 to do besides those canceled and x equals 148  and you're done so this star cast of 148 degrees and you can check yourself 148 - 72 / - should be 38 okay number 8 they label both Arts are vortexes on the outside so we're going to subtract so we would say this Arc - this Arc / equals the single set that up exactly like you say it and again you can do the 1/2 in front where you can do that divided by 2 if do the 4X Plus 8 when I go to - and there's more than one thing there you have to keep that parentheses 3x + 2 + if you want to put that in a princi divided by 2 equals 28 now I think it's easier to get up this way because you just multiply that too but at 28 to get rid of it now when I do that the two times the 28th that gives 56  now that too is gone we have this okay now minus currency what do you have to do when you have minus in front of a prince you have to distribute that negative so that Megan is going to go with the 3x and it's going to go with it too so what I'm going to have is the for x + 8  then minus the 3x and then minus the two so you change both science basically is what now you want to collect like terms - 4 x - the 3x his X and then the 8-2 is going to give me 6 and I still have equals 56 now subtract the six from both sides and x equal 50 degrees so you would put a 50 here for that x50 here for that Axe and you could find both of those arcs  okay number 9 for each angle and Arc that you can find no you can't find every single one but you can find most of them  I want first things you want to realize is you fun these without knowing anything that's 45 this is vertical so that is 45 degrees and then you can find these two by using Y linear pairs so if you subtract from 180 you get on 35 degrees and 135 degrees now none of these are single so we don't have an angle in her Arc that are equal none of these are inscribed angles we don't have any vert x's on the the circle so we have a Vertex on the outside and we have a Vertex on the inside okay let's look at the one on the inside we know one art we know the angle can we find the other Arc yes because we know 60 + this art divided by 2 equals 45 so we going to have to do a little algae we know 60 plus we'll make that Arc we don't know x divided by 2 equals 45 now 2 * 45 is 9 60 + x subtract 60 from both sides and x equals 30 so we know first evolve the dis Arc is 30 degrees now  the other thing is we know this thing was 1:35 but we would have to either that Arc or this art and we don't know this whole Arc and we don't know this our cat off so we can't use these angles to do that but let's look at this 30 okay this intersects on the outside it makes this Ark  and it makes this Arc  K will this art would be the 80 plus the 30 so that's 110 degrees if we know one Ark and the angle we can find the one missing Ark we got to do her algebra again so the Big Arc is 110 minus the little Ark we don't know / 2 equals 30 degrees the angle all right two times 30 you get 110 - 6 60 then we're going to subtract the 110 from both sides and 60 - 110 is 50 negative 50 equals negative X so x equals a positive 50 so now we know that this Ark is 50 degrees now  we don't know this our core this art so we can't do 360 - anything that is everything we can find week everything here except for this art and this art we could even label these angles that's 30 degrees and then 30-1 80 is 150 degrees here and here okay so remember if a Vertex is on the circle then it's half of the Ark  can I say vertex is inside the circle you add the two arts and divide two or take half if the vertex is on the outside you do Big Arc minus small Arc / 2 or take half equals angle and that's what you need to know for this lesson

Uploaded by Pam Chastain.

Video Gallery

10.5 Notes AP

Popular Videos