What are Complementary and Supplementary Angles in Geometry? - [5] - Free Educational videos for Students in K-12

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

Transcript


00:00	Hello . Welcome back . The title of this lesson
00:02	is called finding missing angles . This is part one
00:05	. We also call this lesson understanding complementary angles and
00:09	supplementary angles . So this is more of a geometry
00:12	lesson but it's really you know , it gives a
00:14	lot of students problems but I promise we're gonna break
00:16	it down . So it's very , very simple .
00:18	The name's complementary and supplementary angles come up a lot
00:21	. They have big words , They seem difficult .
00:23	We're gonna make it very very simple for you first
00:25	. Let's go back and talk about a 90° angle
00:28	. We've been using 90° angles a lot and we
00:31	have a 90° angle right here . Now forget about
00:33	this this line right here . Just forget about that
00:36	. Look at this ray connected at a vertex here
00:40	to this ray . These are what we call 90
00:42	degrees here . And the reason you know it's 90
00:45	degrees is because there's the square thing in the corner
00:47	. So again , forget about this raid . Just
00:49	forget about it . That we have a little square
00:51	in the corner . And that means that it's an
00:53	exact measure of 90 degrees . Right ? That 90
00:57	degree angle has a special name . We call it
00:59	a right angle . So this is a right angle
01:02	. Right now , we understand the concept of a
01:05	right angle . We need to talk about what we
01:07	call a complimentary angle , right ? Sounds card is
01:10	very , very simple . All it means is that
01:12	if we know that this measure of the angle is
01:15	90 degrees , right ? So I can actually draw
01:17	it here . We know that the measure here ,
01:19	this entire angle here that goes from here to here
01:22	because we're measuring all the way from here to here
01:24	. We know that this thing is 90 degrees .
01:27	How do we know ? Because we have this little
01:28	symbol in the corner , Right ? So if it's
01:30	90 degrees , then it means that the measure of
01:33	this angle number one measured from this ray to this
01:36	ray , plus whatever the measure of this race angle
01:39	is to this ray , we add this angle and
01:42	added to this angle . It has to be equal
01:44	to 90 degrees . How do we know ? Because
01:46	we know that it's a right angle which has a
01:49	measure of 90 degrees . So all it's basically saying
01:52	is that if you know what the total angle measure
01:54	is and it's 90 degrees . Then if you split
01:57	that angle into two smaller angles , if you like
02:00	chop it up , then you know that if you
02:02	add these two , these two inner angles together ,
02:04	they must equal 90 degrees . When you have two
02:07	angles that add up an equal 90 degrees . We
02:10	call it a complimentary angle . This is not a
02:14	compliment . Like giving somebody a compliment . Like ,
02:16	hey , your hair is nice or your shoes look
02:18	good . Today is not that kind of compliment in
02:20	geometry and math . We call a complimentary angle angles
02:23	that add to 90 degrees . So this thing down
02:26	here looks really complicated . But now that you know
02:28	what it means in words it's not complicated . This
02:31	means the measure of angle one . That's what the
02:33	M means measure of angle one plus the measure of
02:37	angle to whatever these angles are , they must add
02:40	up to be 90 degrees . Now we've drawn it
02:43	so that this angle is cut basically in half ,
02:46	almost in half . So angle one and angle to
02:48	we're going to be about the same . But whatever
02:50	angle one and two are , they must add to
02:52	90 degrees . So in your mind When they add
02:55	to 90°, , we call it a complimentary angle .
02:58	And then we also have learned that the overall angle
03:00	and we have this symbol in the quarter when it's
03:02	exactly 90° is called a right angle . So right
03:06	angle is whenever you have two smaller angles inside that
03:10	are complementary when they add up to 90° than the
03:13	overall larger angle is what we call a right angle
03:16	. And that is what we call complementary smaller angles
03:19	there when they add to 90 . Now we want
03:21	to talk about the other case . So we have
03:23	a special name when an angle is 90 degrees ,
03:27	we call it a right angle . Now we also
03:29	have a special name when the angle is exactly 180
03:33	degrees . Now , if you think about it ,
03:35	forget about this part of the diagram , forget about
03:36	this . If you have an angle measure where it
03:39	goes straight up and down , this is what we
03:40	call 90 degrees , it goes straight up and down
03:42	, perpendicular exactly up and down is what we call
03:45	90 degrees . Now from this point , if we
03:47	go another 90 degrees , then we're gonna be measuring
03:50	an angle that doesn't stop here . It goes all
03:53	the way . I want you to ignore this for
03:55	now it goes all the way to the Kind of
03:57	the other horizon . When you have two angles that
04:00	are completely or one angle that is like measured from
04:03	one ray this way and one ray completely the opposite
04:06	direction . That's called a 180° angle . Why ?
04:10	Because if you think about it straight up and down
04:13	is 90 degrees . So if I go another 90
04:15	degrees , 90 plus 90 nine plus nine is 18
04:19	, right , 90 plus 90 is 180 . So
04:23	this entire angle that goes over here is actually 180
04:27	degrees . So I want to measure that by kind
04:30	of drawing this right here . If I got a
04:32	protractor out and measured the angle from this ray .
04:36	There's a vertex here all the way over here .
04:38	This is 180°. . Now that angle of 180 has
04:43	a special name , we call it a straight angle
04:46	. Why do you think it's called a straight angle
04:48	? Well , it's because the lines that make up
04:50	the angle of the raise that make up the angle
04:51	formed like a straight line like this . So a
04:53	straight angle is a 180 degree angle . A right
04:57	angle is a 90 degree angle . And of course
05:00	You have to put 2 90° angles together to get
05:03	the straight angle of 180°. . Now , if we
05:07	know that this angle is 180 degrees . And if
05:10	we chop this angle up into two smaller angles ,
05:13	angle number one , in angle number two , then
05:15	we know that whatever angle one is . If we
05:19	add to whatever angle to is , it must add
05:21	up to 180 degrees because we know what the total
05:24	angle is , Right . So if we add up
05:27	the measure of angle one plus the measure of angle
05:30	too , and we get an angle of 180°, ,
05:33	then those are called supplementary angles . So the bottom
05:38	line is supplementary angles are two angles so that when
05:41	you put them together they add up to exactly 180°,
05:47	, not 181 , not 179 , 180.4 , it
05:51	has to add exactly to 180°. . Then we call
05:55	them supplementary angles . If the two angles add up
06:00	to exactly 90 degrees , we call them complementary angles
06:03	. So these are important terms complementary angles or any
06:07	two angles that add up to give you 90 degrees
06:09	and supplementary angles or any two angles that add up
06:12	to give you 180 degrees right . And then we
06:16	looked at the idea of a straight angle . A
06:19	straight angle just means it's 180 degrees because it forms
06:22	kind of the straight line when you measure the angle
06:24	between them . A right angle of course is a
06:26	90 degree angle that goes kind of up and down
06:29	perpendicular like this , if you slice a right angle
06:33	into smaller angles , then those angles are complementary to
06:36	add up to 90 . If you slice a straight
06:39	angle into smaller angles , then those angles must add
06:42	up to 180 which makes them supplementary . So that's
06:45	all the background material and all of that is going
06:48	to make the next part of the problem is very
06:50	, very simple . Let me give you a diagram
06:52	like this and I ask you what is the measure
06:56	of angle X . And when I say the measure
06:59	of angle X , I don't mean like this whole
07:01	thing . I mean the measure of angle X goes
07:03	from here to this ray right there . How do
07:05	I find that angle measure ? Well , I could
07:08	get a protractor and I can measure it but we
07:11	have enough information to figure it out just from the
07:13	diagram Because we know that this entire angle is what
07:18	this symbol means . 100 , I'm sorry , 90°.
07:21	. So the measure of the angle from here ,
07:23	all the way to here is 90°. . How do
07:27	I know it's 90°. . It's because this symbol tells
07:29	me that this angle is a 90° angle And I
07:32	know that this angle is 31°. . So if I
07:34	start from 90 And I take away or subtract the
07:38	31° from 90 , then whatever is left over must
07:41	be ex . So what I have to do is
07:44	say well I'm gonna start with 9° and I'm gonna
07:47	subtract away 31 degrees . It becomes a very simple
07:50	subtraction problem . So what do we do ? We
07:54	try to say zero minus one ? We can't do
07:56	that . So we make us a 10 . And
07:58	to do it we make the nine into an eight
08:01	, 10 minus one is nine and eight minus three
08:04	is what ? 55 there ? So what do we
08:07	get ? 59 degrees ? The measure of angle X
08:10	must be 59 degrees . How do we know ?
08:15	It has to be 59 degrees . First of all
08:17	, notice that 59 degrees is bigger than 31 degrees
08:20	. That makes sense because the measure of this angle
08:23	looks to be from the drawing anyway , it looks
08:25	to be a little bit bigger than the angle over
08:28	here . It's it's wider like this , Right ?
08:31	How do we know that ? That's correct . Let's
08:32	just check it real quick . We know that if
08:35	this is true , the 59 degree angle that we
08:37	get . If we add it to the 31 degree
08:40	angle , if we add it , we should get
08:42	90 because these are what we called complementary angles ,
08:46	complementary means we add to 99 plus one is 10
08:50	and then we have +56789 and they add to 90
08:53	degrees . So we check . So when you have
08:55	a diagram and you're asked to find a missing angle
08:58	most of the time . all you have to do
09:00	is figure out what you need to subtract from what
09:03	and you have to know the idea of a complimentary
09:05	angle and a supplementary angle . So let's put some
09:07	more of these diagrams on the board and get a
09:09	little more practice . All right , so here's problem
09:13	number two . We're looking for the measure of angle
09:16	W . Angle W . Is the angle measured from
09:19	this ray to this ray right here . What is
09:22	that angle measure ? How do we figure it out
09:24	? Well , we know that the 26 degree angle
09:27	here must be what we call supplementary to the angle
09:31	W supplementary means they add up to 180 degrees .
09:35	How do we know this ? Because we know that
09:37	this larger angle is a straight angle it goes and
09:40	measure from this ray all the way over to this
09:42	and we know it's a straight angle . Not because
09:44	there's a special symbol on the paper , but because
09:47	it forms a straight line . When you have An
09:49	angle that is basically formed from a straight line like
09:52	this , then you know , it has to be
09:53	180°. . That's part of what we're learning here .
09:56	So because the larger angle is 180°, , we'll just
09:59	subtract off this 26° angle and figure out what is
10:03	left over . So what we'll do then is we'll
10:06	start with the 180 degree angle , the straight angle
10:09	, the larger angle . And we'll subtract off this
10:12	26 degree angle which is smaller and whatever is left
10:16	over must be the measure of angle W So let's
10:19	do this , subtraction . What is zero minus six
10:21	. What ? We can't do that . So we
10:22	borrow make that a 10 And to do it .
10:25	The eight then becomes a seven . So what is
10:28	10 minus six ? 10 minus six is four and
10:31	seven minus two is five and one minus zero is
10:35	one . So the angle of measure W . Is
10:38	154 degrees . How did we know to do this
10:42	? Well , we know that any straight angle is
10:44	180 degrees . And then we subtract off the 26
10:47	degree angle whenever is left over is the measure of
10:50	angle W . And then we know that if we
10:52	take the 154 and we add it to the 26
10:56	then we know we're going to get 180 degrees .
10:58	Try it on a separate sheet of paper because we
11:00	know that these angles are supplementary to each other ,
11:03	supplementary means they add to 180 degrees . All right
11:08	, let's take a look at Problem three . We
11:10	want to find a measure of angles . E how
11:12	do we do it ? What we know what this
11:14	larger angle is . The larger angle is a 90
11:17	degree angle because of the symbol here . So we'll
11:19	start with the measure of 90° and we'll just subtract
11:23	off the 72° angle here and whatever is left over
11:27	must be Z . So we'll take the 90°, ,
11:29	we'll subtract the 72° and see what we get .
11:34	So zero minus two , this becomes a 10 ,
11:37	the nine becomes an eight , the 10 minus two
11:40	becomes in eight and eight minus seven becomes a one
11:45	. And so the angle Z becomes 18 degrees .
11:49	Because we know if we start from 90 and we
11:51	subtract 72 , we get 18 , which is a
11:53	very small angle . It makes sense That this is
11:55	much smaller because it looks to be a much smaller
11:58	angle than the 72° angle here . And we know
12:01	that 18 plus the 72 must equal the 90 because
12:05	these are complementary angles . I keep saying the words
12:08	over and over again because I want you to remember
12:10	complementary means they add to 90 , supplementary means they
12:14	add to 180 . All right , here's problem #
12:18	four . What is the measure of angle V .
12:22	Same thing . We have a straight angle here .
12:24	The straight angle is 180 degrees . So we'll take
12:27	the 180 we'll subtract off the 119 which we are
12:30	given their and whatever is left over , we'll subtract
12:34	the 119 . Whatever's leftover must be the missing angle
12:37	V . So what do we have here ? Zero
12:40	minus nine . This becomes a 10 . We borrow
12:43	to make this a seven . And what do we
12:45	have here ? We have 10 minus nine is 17
12:49	minus one is six and one minus one is zero
12:52	. So the angle of measure V is 61 degrees
12:56	measure of angle V is 61 degrees . All right
13:00	. Here's our last problem for this lesson . We
13:02	want to find the measure of angle H . We
13:05	know that we have a straight angle which is 180
13:08	degrees exactly . So start with 100 and 80 and
13:10	subtract off the 65 degree angle here . Whatever is
13:13	left over must be H . 180 minus 65 .
13:19	What do we get ? We have to borrow .
13:22	This becomes a 10 , this becomes a seven and
13:25	then we have 10 minus five is five and seven
13:28	minus six is one and one minus zero is one
13:32	. And so we get an answer of , let
13:35	me just check myself here , 115° 115°. . The
13:41	measure of Angle H . Now does it make sense
13:43	? We're saying that the angle H is much bigger
13:45	than this angle here and it makes sense because this
13:47	looks to be a larger angle than the 65 degree
13:49	angle and we know if we add 115 with the
13:53	65 we're going to get 180 degrees because these are
13:56	supplementary angles . So again supplementary means The two angles
14:00	add to 180 And complementary means the two angles add
14:05	to 90 , right ? So you see the problems
14:07	here become very simple once you know what to do
14:10	and that's what it always is in math , it's
14:12	hard in the beginning , but then once you know
14:14	what to do becomes easier and easier . The only
14:16	thing here you have to understand is what isn't a
14:19	complimentary set of angles and what is a supplementary set
14:21	of angles . What's a straight angle And what is
14:24	a right angle ? So make sure you can get
14:26	these yourself , practice them , solve all of them
14:28	yourself , following onto part two , we'll get a
14:30	little more practice .

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