hi there geometers i am here to talk you through the angle addition postulate what it is what it means how we use it and give you some examples so first of all the angle addition postulate assumes you have an angle let's go ahead and name my angle angle abc okay and it's like if you haven't seen my video on segment edition postulate you might want to look at that because i'm going to make some comparisons here the segment addition postulate and angle addition postulate say very similar things one's about segments one's about angles and like the segment addition postulate it sort of goes with the idea of between in terms of the setup here's what i mean you have an angle and then you have a point that is in the interior of the angle okay like let's call this point point f okay and what that does is that sets up a situation where you could draw a ray that goes from the vertex of your angle through point f and that ray is between the two rays that make up the original angle so you pretty much just have one bigger angle split into two smaller pieces by this ray that goes through it now we are not implying that that ray goes right through the middle i'm not saying that's the angle bisector it just goes through somewhere it may not be right in the middle of this angle and therefore we're not going to make any assumptions that it is okay and so what we have is we have this situation where the smaller two angles then abf and fbc remember to name an angle with three letters we start with one side go to the vertex and then go out the other side always have to have the vertex second so i could have named this angle a b f or i could have named it f b a but b has to be in the middle so a b f and f b c [Music] together make up the entire angle okay so now what i just wrote is actually incorrect it's not incorrect in terms of what we're saying it's incorrect notation wise because what we're really going to talk about here is it's the measure of the smaller two angles the measure of this angle however many degrees this angle is and the measure of this angle however many degrees between here have to add up to the number of degrees or the measure of the big angle so we're going to use little m's to be accurate so the measure of one smaller angle plus the measure of the other smaller angle equals the measure of the whole bigger angle and another way we can think of that just like segment addition postulate is that one part plus the other part equals the whole thing the whole angle is the sum of its parts okay so that can be useful if we're trying to find things like missing angle measures or trying to solve equations so in our first example i wrote this through this little angle well multiple angles um we have three angles here we've got the whole big one and then we've got each of the two smaller ones so let's suppose that i am given this information about these angles okay so i am told that the measure of angle t ms which you could think of let's go ahead and do this you could think of it as this angle right here that's tms is 12 degrees and l m t which i'm going to think about like this this whole angle all the way across that's l m t so lmt is the whole big one is 39 degrees and i'm supposed to find lms which is this part right here that's the leftover part okay so let me just make a squiggle these are not congruence markings okay this is just me trying to show where that angle is okay so again we've got part plus part equals whole and in this particular case the two smaller parts are the two smaller angles are and let's go from this side l m s so the measure of angle l m s plus s next smaller one the one that's sort of pinkish here s m t the measure of angle s m t is equal to the whole thing which is l m t l m t okay so that is how i can set up my equation and i'm just going to substitute in this information that i was given tms is the same as smt okay you could turn the angle name around as long as you keep the vertex in the middle so this is 12. lmt is 39 and the one we don't know let's just call x we don't know the measure of angle lms that's what we're being asked for in our problem so here's my equation the angle addition postulate just pretty much told me how to set up the equation so that i can find that missing angle and i'm going to subtract now that i have an equation i just have to pull out my equation solving skills and i will be able to get the answer so x is 27 so in other words going back we've got this was 12 degrees and this is 27 degrees and then we can sort of check ourselves here not really sort of we can check ourselves here 27 plus 12 has to add up to the entire angle and that's 39 and that is correct so my answer for x was 27 and in this case x stood for lms so that was what i was trying to find anytime you solve an equation you have to check and say is the variable what i was trying to find or do i have to maybe go back and plug it in but here the variable stood for the entire angle and it was the one that we were trying to find so there's nothing left to plug in okay let's look at another example like that one that's perhaps a little bit more algebraic let's suppose i have this figure and i am told that i have this info okay i know that the measure of angle m n p m n p i don't think that's too far over there we go m and p is 3x p and r p n r is 2 x minus 6 and m n r that's the whole big one is and i can see that these two smaller angles here add up to the whole or make up the whole big angle so it will be an angle addition postulate situation where the two smaller parts make up the entire angle okay um now i did not write this completely accurately on purpose because i wanted to show it to you guys sometimes this confuses people notice that i didn't put degree symbols up here um because it's not just a number if i wanted to add the degree symbol which is something i need because we measure angles and degrees so it will be in degrees i really need parentheses now a lot of teachers aren't going to be mad at you if you don't put parentheses and you put a degree symbol there but i just want you to understand why sometimes they do that is they're saying this whole thing is a number and it's that many degrees in other words there's nothing special about those parentheses they're just there because it's kind of technically inaccurate to put the degree symbol beside something that's not a number okay so now we're ready to start setting up our equation and we use the angle addition postulate to set up our equation so we have part plus part equals whole in this case one part is mnp and just like i said in the segment addition postulate you don't necessarily have to write everything i'm writing now the next part is pnr and this is really just like if your teacher asks you to write an equation to show how it's set up then yeah write it if you like to write it because it helps you solve the problem write it otherwise you don't have to the whole thing is the measure of mnr and now i'm going to substitute this information i was given mnp is 3x plus pnr is 2x minus 6 equals mnr is 44. so now i have an equation i can solve and i've got three x's and two x's is five x's and i solve my equation just like any other equation and i get x is 10. now perfect example of here i got the value of my variable but i'm not sure if that's what's being asked for i didn't actually tell you what's being asked for so this is where however i would go ahead and say is that what i was needing do i was i asked to find x or find the value of the variable or was i maybe asked something like find the measure of angle mnp if i was asked to find the measure of angle mnp i need to take this 10 and go put it in to m and p and i get 3 times x becomes 3 times 10 which is 30 degrees might have also it could have asked me for angle pnr pnr 10 plugged in here would give me 2 times 10 is 20 minus 6 20 minus 6 is 14 degrees and here again we get to sort of check ourselves because 30 plus 14 it does add up to 44. so it all makes sense and we must have done it right i hope this helped and i'll see you again next time