What are Complementary and Supplementary Angles in Geometry? - [5]

hello welcome back the title of this lesson is called finding missing angles this is part one we also call this lesson uh understanding complementary angles and supplementary angles so this is more of a geometry lesson but it's really you know it gives a lot of students problems but i promise we're going to break it down so it's very very simple the names complementary and supplementary angles come up a lot they have big words they seem difficult we're going to make it very very simple for you first let's go back and talk about a 90 degree angle we've been using 90 degree angles a lot and we have a 90 degree angle right here now forget about this this line right here just forget about that look at this array connected at a vertex here to this ray these are what we call 90 degrees here and the reason you know it's 90 degrees is because there's the square thing in the corner so again forget about this ray just forget about it then we have a a little square in the corner and that means that it's an exact measure of 90 degrees right that 90 degree angle has a special name we call it a right angle so this is a right angle right now we understand the concept of a right angle we need to talk about what we call a complementary angle right sounds card is very very simple all it means is that if we know that this measure of the angle is 90 degrees right so i can actually draw it here we know that the measure here this entire angle here that goes from here to here because we're measuring all the way from here to here we know that this thing is 90 degrees how do we know because we have this little symbol in the corner right so if it's 90 degrees then it means that the measure of this angle number one measured from this ray to this ray plus whatever the measure of this rays angle is to this ray we add this angle and add it to this angle it has to be equal to 90 degrees how do we know because we know that it's a right angle which has a measure of 90 degrees so all it's basically saying is that if you know what the total angle measure is and it's 90 degrees then if you split that angle into two smaller angles if you like chop it up then you know that if you add these two in these two inner angles together they must equal 90 degrees when you have two angles that add up an equal 90 degrees we call it a complementary angle this is not a complement like giving somebody a compliment like hey your hair is nice or your shoes look good today it's not that kind of compliment in geometry and math we call a complementary angle angles that add to 90 degrees so this thing down here looks really complicated but now that you know what it means in words it's not complicated this means the measure of angle one that's what the m means measure of angle 1 plus the measure of angle 2 whatever these angles are they must add up to be 90 degrees now we've drawn it so that this angle is cut basically in half almost in half so angle 1 and angle 2 are going to be about the same but whatever angle 1 and 2 are they must add to 90 degrees so in your mind when they add to 90 degrees we call it a complementary angle and then we also have learned that the overall angle when we have this symbol in the corner when it's exactly 90 degrees is called a right angle so right angle is whenever you have two smaller angles inside that are complementary when they add up to 90 degrees then the overall larger angle is what we call a right angle and that is what we call complementary smaller angles there when they add to 90. now we want to talk about the other case so we have a special name when an angle is 90 degrees we call it a right angle now we also have a special name when the angle is exactly 180 degrees now if you think about it forget about this part of the diagram forget about this if you have an angle measure where it goes straight up and down this is what we call 90 degrees it goes straight up and down perpendicular exactly up and down is what we call 90 degrees now from this point if we go another 90 degrees then we're going to be measuring an angle that doesn't stop here it goes all the way i want you to ignore this for now it goes all the way to the kind of the other horizon when you have two angles that are completely or one angle that is like measured from one ray this way and one ray completely the opposite direction that's called a 180 degree angle why because if you think about it straight up and down is 90 degrees so if i go another 90 degrees 90 plus 90 9 plus 9 is 18 right 90 plus 90 is 180. so this entire angle that goes over here is actually 180 degrees so i want to measure that by kind of drawing this right here if i got a protractor out and measured the angle from this ray there's a vertex here all the way over here this is 180 degrees now that angle of 180 has a special name we call it a straight angle why do you think it's called a straight angle well it's because the the lines that make up the angle the rays that make up the angle form like a straight line like this so a straight angle is a 180 degree angle a right angle is a 90 degree angle and of course you have to put two 90 degree angles together to get the straight angle of 180 degrees now if we know that this angle is 180 degrees and if we chop this angle up into two smaller angles angle number one in angle number two then we know that whatever angle one is if we add it to whatever angle two is it must add up to 180 degrees because we know what the total angle is right so if we add up the measure of angle 1 plus the measure of angle 2 and we get an angle of 180 degrees then those are called supplementary angles so the bottom line is supplementary angles are two angles so that when you put them together they add up to exactly 180 degrees not 181 not 179 not 180.4 it has to add exactly to 180 degrees then we call them supplementary angles if the two angles add up to exactly 90 degrees we call them complementary angles so these are important terms complementary angles are any two angles that add up to give you 90 degrees and supplementary angles or any two angles that add up to give you 180 degrees right and then we looked at the idea of a straight angle a straight angle just means it's 180 degrees because it forms kind of this straight line when you measure the angle between them a right angle of course is a 90 degree angle that goes kind of up and down perpendicular like this if you slice a right angle into smaller angles then those angles are complementary to add up to 90. if you slice a straight angle into smaller angles then those angles must add up to 180 which makes them supplementary so that's all the background material and all of that is going to make the next part of the problems very very simple let me give you a diagram like this and i ask you what is the measure of angle x and when i say the measure of angle x i don't mean like this whole thing i mean the measure of angle x goes from here to this ray right there how do i find that angle measure well i could get a protractor and i can measure it but we have enough information to figure it out just from the diagram because we know that this entire angle is what this symbol means 100 i'm sorry 90 degrees so the measure of the angle from here all the way to here is 90 degrees how do i know it's 90 degrees it's because this symbol tells me that this angle is a 90 degree angle and i know that this angle is 31 degrees so if i start from 90 and i take away or subtract the 31 degrees from 90 then whatever is left over must be x so what i have to do is say well i'm going to start with 9 degrees and i'm going to subtract away 31 degrees it becomes a very simple subtraction problem so what do we do we try to say 0 minus 1. we can't do that so we make this a ten and to do it we make the nine into an eight ten minus one is nine and eight minus three is what five five there so what do we get 59 degrees the measure of angle x must be 59 degrees how do we know it has to be 59 degrees first of all notice that 59 degrees is bigger than 31 degrees that makes sense because the measure of this angle looks to be from the drawing anyway it looks to be a little bit bigger than uh the angle over here it's it's wider like this right how do we know that that's correct let's just check it real quick we know that if this is true the 59 degree angle that we get if we add it to the 31 degree angle if we add it we should get 90 because these are what we called complementary angles complementary means we add to 90. 9 plus 1 is 10 and then we have 5 6 7 8 9 and they add to 90 degrees so we check so when you have a diagram and you're asked to find a missing angle most of the time all you have to do is figure out what you need to subtract from what and you have to know the idea of a complementary angle and a supplementary angle so let's put some more of these diagrams on the board and get a little more practice all right so here's problem number two we're looking for the measure of angle w angle w is the angle measured from this ray to this ray right here what does that angle measure how do we figure it out well we know that the 26 degree angle here must be what we call supplementary to the angle w supplementary means they add up to 180 degrees how do we know this because we know that this larger angle is a straight angle it goes and measure from this ray all the way over to this and we know it's a straight angle not because there's a special symbol on the paper but because it forms a straight line when you have an angle that is basically formed from a straight line like this then you know it has to be 180 degrees that's part of what we're learning here so because the larger angle is 180 degrees we'll just subtract off this 26 degree angle and figure out what is left over so what we'll do then is we'll start with the 180 degree angle the straight angle the larger angle and we'll subtract off this 26 degree angle which is smaller and whatever is left over must be the measure of angle w so let's do this subtraction what is 0 minus 6 well we can't do that so we borrow make that a 10 and to do it the 8 then becomes a 7. so what is 10 minus 6 10 minus 6 is 4 and 7 minus 2 is 5 and 1 minus 0 is 1. so the angle of measure w is 154 degrees how did we know to do this well we know that any straight angle is 180 degrees and then we subtract off the 26 degree angle whatever's left over is the measure of angle w and then we know that if we take the 154 and we add it to the 26 then we know we're going to get 180 degrees try it on a separate sheet of paper because we know that these angles are supplementary to each other supplementary means they add to 180 degrees all right let's take a look at problem three we want to find the measure of angle z how do we do it well we know what this larger angle is the larger angle is a 90 degree angle because of the symbol here so we'll start with the measure of 90 degrees and we'll just subtract off this 72 degree angle here and whatever is left over must be z so we'll take the 90 degrees we'll subtract the 72 degrees and see what we get so 0 minus 2 this becomes a 10 the 9 becomes an 8. the 10 minus 2 becomes an 8 and a 8 minus 7 becomes a 1. and so the angle z becomes 18 degrees because we know if we start from 90 and we subtract 72 we get 18 which is a very small angle it makes sense that this is much smaller because it looks to be a much smaller angle than the 72 degree angle here and we know that 18 plus the 72 must equal the 90 because these are complementary angles i i keep saying the words over and over again because i want you to remember complementary means they add to 90 supplementary means they add to 180. all right here's problem number four what is the measure of angle v same thing we have a straight angle here this straight angle is 180 degrees so we'll take the 180 and we'll subtract off the 119 which we are given there and whatever's left over we'll subtract the 119 whatever's left over must be the missing angle v so what do we have here zero minus nine this becomes a ten we borrow to make this a seven and what do we have here we have ten minus nine is one seven minus one is six and 1 minus 1 is 0 so the angle of measure v is 61 degrees measure of angle v is 61 degrees all right here's our last problem for this lesson we want to find the measure of angle h we know that we have a straight angle which is 180 degrees exactly so start with 180 and subtract off the 65 degree angle here whatever is left over must be h 180 minus 65 what do we get we have to borrow this becomes a ten this becomes a seven and then we have ten minus five is five and seven minus six is one and one minus zero is one and so we get an answer of let me just check myself here 115 degrees 115 degrees the measure of angle h now does it make sense we're saying that the angle h is much bigger than this angle here and it makes sense because this looks to be a larger angle than the 65 degree angle and we know if we add the 115 with the 65 we're going to get 180 degrees because these are supplementary angles so again supplementary means the two angles add to 180 and complementary means the two angles add to 90 right so you see the problems here become very simple once you know what to do and that's what it always is in math it's it's hard in the beginning but then once you know what to do it becomes easier and easier the only thing here you have to understand is what isn't a complementary set of angles and what is a supplementary set of angles what's a straight angle and what is a right angle so make sure you can get these yourself practice them solve all of them yourself following on to part two we'll get a little more practice

Channel: Math and Science

Views: 18,712

Keywords: complementary angles, supplementary angles, complementary and supplementary angles, complementary angle theorem, supplementary and complementary angles, supplementary angles solve for x, geometry, angles, geometry angle relationships, geometry angles solve for x, geometry angle measures, geometry angle pairs, geometry angle theorems, what are complementary angles, vertical angles, adjacent angles, right angle, angle problems, trigonometry, math, math practice, right triangle, tutor

Id: otF13ROdJ-U

Length: 14min 34sec (874 seconds)

Published: Tue Dec 08 2020