Main content
7th grade
Course: 7th grade > Unit 6
Lesson 3: Vertical, complementary, and supplementary angles- Angles: introduction
- Name angles
- Complementary & supplementary angles
- Vertical angles
- Identifying supplementary, complementary, and vertical angles
- Complementary and supplementary angles (visual)
- Complementary and supplementary angles (no visual)
- Complementary and supplementary angles review
- Vertical angles
- Finding angle measures between intersecting lines
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Complementary & supplementary angles
CCSS.Math:
Learn about complementary and supplementary angles, as well as the definitions of adjacent and straight angles. Created by Sal Khan.
Want to join the conversation?
- Do complementary and supplementary angles have to be adjacent?(72 votes)
- They don't have to be adjacent but if they are they form a straight line on the sides that they don't share.(20 votes)
- Does anyone have any hacks for remembering this I have a test on Friday(26 votes)
- Try this:
Complementary angles add up to 90°
- example: 15° & 75° are complementary
(added together, they form a right angle)
-and-
Supplementary angles add up to 180°
- example: 50° & 130° are supplementary
(added together, they form a straight line)
Two facts:
(1) 90° comes before 180° on the number line
(2) "C" comes before "S" in the alphabet
You can use this to help you remember!
90° goes with "C" for complementary
so complementary angles add up to 90°
180° goes with "S" for supplementary
so supplementary angles add up to 180°
Hope this helps!(137 votes)
- Definition of linear pair?(10 votes)
- Two angles are linear if they are adjacent angles formed by two intersecting lines. A straight angle is 180 degrees so 2 linear pairs of angles must always add up to 180 degrees.
Hope that this is helpful to u(5 votes)
- So how do you know if its complementary(7 votes)
- If two angles add up to 90 degrees then they are complementary, if they add up to 180 degrees they they are supplementary(6 votes)
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⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢹⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣄⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡟⢶⣄⠀⠀⠀⠀⠀
⠯⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠈⠳⠀⠀⠀⠀
⠀⠀⢀⣀⣀⡀⣼⣤⡟⣬⣿⣷⣤⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⣉⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣄⠀⣀⣀⡀(12 votes) - Do we have names for angles that add up to 270 and 360 degrees?(3 votes)
- There are currently no name for 2 angles that add up to 270 degrees but Explementary Angles are the name for a pair of angles that adds up to 360 degrees, even if an angle is more than 180 degrees
Hope that this is helpful(10 votes)
- Is there a video about the angle pairs, specifically? Because I don't remember seeing anything about it.(6 votes)
- I think this is the only one. A pair is a group of two. So a pair of angles = two angles.(6 votes)
- Let's say I have an angle ABC, and it 0:00looks something like this. 0:03So its vertex is going to be at B. Maybe 0:05A sits right over here, and C sits right over there. 0:09And then also let's say that we have another angle called DBA. 0:14I want to have the vertex once again at B. So let's 0:22say it looks like this. 0:26So this right over here is our point D. That is our point D. 0:27And let's say that we know that the measure of angle DBA 0:33is equal to 40 degrees. 0:39So this angle right over here, its measure 0:41is equal to 40 degrees. 0:43And let's say that we know that the measure of angle ABC 0:45is equal to 50 degrees. 0:50So there's a bunch of interesting things happening 0:55here. 0:57The first interesting thing that you might realize 0:58is that both of these angles share a side. 1:00If you view these as rays-- they could be lines, line segments, 1:03or rays-- but if you view them as rays, 1:06they both share this ray BA. 1:08And when you have two angles like this 1:11that share the same side, these are called adjacent angles. 1:13Because the word "adjacent" literally means next to. 1:16These are adjacent. 1:21They are adjacent angles. 1:23Now there's something else that you 1:26might notice that's interesting here. 1:27We know that the measure of angle DBA is 40 degrees 1:29and the measure of angle ABC is 50 degrees. 1:32And you might be able to guess what the measure of angle DBC 1:35is. 1:40If we drew a protractor over here-- 1:44I'm not going to draw it. 1:46It will make my drawing all messy. 1:47Well, maybe I'll draw it really fast. 1:49So if you had a protractor right over here, 1:51clearly this is opening up to 50 degrees. 1:52And this is going another 40 degrees. 1:55So if you wanted to say what the measure of angle DBC is, 1:57it would essentially be the sum of 40 degrees and 50 degrees. 2:01And let me delete all of this stuff 2:04right here to keep things clean. 2:06So the measure of angle DBC would be equal to 90 degrees. 2:07And we already know that 90 degrees is a special angle. 2:13This is a right angle. 2:16There's also a word for two angles whose sum add up 2:22to 90 degrees, and that is complementary. 2:26So we can also say that angles DBA and angles 2:30ABC are complementary. 2:38And that is because their measures add up to 90 degrees. 2:46So the measure of angle DBA plus the measure of angle ABC 2:50is equal to 90 degrees. 2:57They form a right angle when you add them up. 3:00And just as another point of terminology 3:03that's kind of related to right angles, 3:05when a right angle is formed, the two rays 3:09that form the right angle or the two lines that 3:12form that right angle or the two line segments that 3:14form that right angle are called perpendicular. 3:17So because we know that measure of angle DBC is 90 degrees 3:19or that angle DBC is a right angle, this tells us, 3:23we know that the line segment DB is 3:28perpendicular to line segment BC. 3:36Or we could even say ray BD is-- instead of using the word 3:46perpendicular, there's sometimes this symbol 3:53right here, which really just shows two perpendicular 3:55lines-- perpendicular to BC. 3:58So all of these are true statements here. 4:02And these come out of the fact that the angle 4:06formed between DB and BC, that is a 90-degree angle. 4:08Now, we have other words when our two angles add up 4:14to other things. 4:17So let's say, for example, I have one angle over here. 4:19Let me put some letters here so we can specify it. 4:31So let's say this is X, Y, and Z. 4:33And let's say that the measure of angle XYZ 4:37is equal to 60 degrees. 4:40And let's say that you have another angle that 4:45looks like this. 4:48And I'll call this, let's say, maybe MNO. 4:52
•Current transcript segment:And let's say that the measure of angle MNO is 120 degrees. 5:02So if you were to add the two measures of these-- so let 5:07me write this down. 5:10The measure of angle MNO plus the measure of angle XYZ, 5:11this is going to be equal to 120 degrees plus 60 degrees, which 5:25is equal to 180 degrees. 5:30So if you add these two things up, 5:32you essentially are able to go all halfway around the circle. 5:35Or you could go throughout the entire half circle 5:38or semicircle for a protractor. 5:41And when you have two angles that add up to 180 degrees, 5:43we call them supplementary. 5:47I know it's a little hard to remember sometimes. 5:4990 degrees is complementary. 5:51They're just complementing each other. 5:52And then if you add up to 180 degrees, 5:54you have supplementary. 5:56You have supplementary angles. 5:58And if you have two supplementary angles that 6:03are adjacent so that they share a common side-- so let 6:05me draw that over here. 6:08So let's say you have one angle that looks like this. 6:10And that you have another angle. 6:13So let me put some letters here again. 6:15And I'll start reusing letters. 6:18So let's say that this is ABC. 6:19And you have another angle that looks like this. 6:23I already used C. 6:31Once again, let's say that this is 50 degrees. 6:36And let's say that this right over here is 130 degrees. 6:39Clearly, angle DBA plus angle ABC, if you add them together, 6:42you get 130 degrees plus 50 degrees, which is 180 degrees. 6:49So they are supplementary. 6:52So let me write that down. 6:53Angle DBA and angle ABC are supplementary. 6:55They add up to 180 degrees. 7:04But they are also adjacent angles. 7:07And because they're supplementary 7:14and they're adjacent, if you look at the broader angle, 7:16the angle used from the sides that they don't have in common. 7:19If you look at angle DBC, this is 7:22going to be essentially a straight line, which 7:29we can call a straight angle. 7:31So I introduced you to a bunch of words here. 7:37And now I think we have all of the tools we 7:39need to start doing some interesting proofs. 7:41And just to review here, we talked about any angles 7:45that add up to 90 degrees are considered to be complementary. 7:50This is adding up to 90 degrees. 7:55If they happen to be adjacent, then the two outside sides 7:56will form a right angle. 8:00When you have a right angle, the two sides of a right angle 8:03are considered to be perpendicular. 8:06And then if you have two angles that add up to 180 degrees, 8:09they're considered supplementary. 8:12And then if they happen to be adjacent, 8:14they will form a straight angle. 8:16Or another way, if you said, if you have a straight angle 8:18and you have one of the angles, the other angle 8:21is going to be supplementary to it. 8:24They're going to add up to 180 degrees. 8:26So I'll leave you there. 8:28(9 votes) - So, complementary is 90 degrees. And supplement is 180 degrees?(6 votes)
- When angles add up to 90 degrees it is complementary, same goes for supplementary, but it needs to equal 180.(6 votes)
Video transcript
Let's say I have an
angle ABC, and it looks something like this. So its vertex is going
to be at B. Maybe A sits right over here, and
C sits right over there. And then also let's say that we
have another angle called DBA. I want to have the vertex
once again at B. So let's say it looks like this. So this right over here is our
point D. That is our point D. And let's say that we know
that the measure of angle DBA is equal to 40 degrees. So this angle right
over here, its measure is equal to 40 degrees. And let's say that we know
that the measure of angle ABC is equal to 50 degrees. So there's a bunch of
interesting things happening here. The first interesting thing
that you might realize is that both of these
angles share a side. If you view these as rays-- they
could be lines, line segments, or rays-- but if you
view them as rays, they both share this ray BA. And when you have
two angles like this that share the same side, these
are called adjacent angles. Because the word "adjacent"
literally means next to. These are adjacent. They are adjacent angles. Now there's something
else that you might notice that's
interesting here. We know that the measure
of angle DBA is 40 degrees and the measure of
angle ABC is 50 degrees. And you might be able to guess
what the measure of angle DBC is. If we drew a
protractor over here-- I'm not going to draw it. It will make my
drawing all messy. Well, maybe I'll
draw it really fast. So if you had a protractor
right over here, clearly this is opening
up to 50 degrees. And this is going
another 40 degrees. So if you wanted to say what
the measure of angle DBC is, it would essentially be the sum
of 40 degrees and 50 degrees. And let me delete
all of this stuff right here to keep things clean. So the measure of angle DBC
would be equal to 90 degrees. And we already know that 90
degrees is a special angle. This is a right angle. There's also a word for
two angles whose sum add up to 90 degrees, and
that is complementary. So we can also say that
angles DBA and angles ABC are complementary. And that is because their
measures add up to 90 degrees. So the measure of angle DBA
plus the measure of angle ABC is equal to 90 degrees. They form a right angle
when you add them up. And just as another
point of terminology that's kind of related
to right angles, when a right angle is
formed, the two rays that form the right angle
or the two lines that form that right angle or
the two line segments that form that right angle
are called perpendicular. So because we know that measure
of angle DBC is 90 degrees or that angle DBC is a
right angle, this tells us, we know that the
line segment DB is perpendicular to
line segment BC. Or we could even say ray BD
is-- instead of using the word perpendicular, there's
sometimes this symbol right here, which really
just shows two perpendicular lines-- perpendicular to BC. So all of these are
true statements here. And these come out of
the fact that the angle formed between DB and BC,
that is a 90-degree angle. Now, we have other words
when our two angles add up to other things. So let's say, for example,
I have one angle over here. Let me put some letters
here so we can specify it. So let's say this
is X, Y, and Z. And let's say that the
measure of angle XYZ is equal to 60 degrees. And let's say that you
have another angle that looks like this. And I'll call this,
let's say, maybe MNO. And let's say that the measure
of angle MNO is 120 degrees. So if you were to add the two
measures of these-- so let me write this down. The measure of angle MNO plus
the measure of angle XYZ, this is going to be equal to 120
degrees plus 60 degrees, which is equal to 180 degrees. So if you add these
two things up, you essentially are able to go
all halfway around the circle. Or you could go throughout
the entire half circle or semicircle for a protractor. And when you have two angles
that add up to 180 degrees, we call them supplementary. I know it's a little hard
to remember sometimes. 90 degrees is complementary. They're just
complementing each other. And then if you add
up to 180 degrees, you have supplementary. You have supplementary angles. And if you have two
supplementary angles that are adjacent so that they
share a common side-- so let me draw that over here. So let's say you have one
angle that looks like this. And that you have another angle. So let me put some
letters here again. And I'll start reusing letters. So let's say that this is ABC. And you have another angle
that looks like this. I already used C. Once again, let's say
that this is 50 degrees. And let's say that this right
over here is 130 degrees. Clearly, angle DBA plus angle
ABC, if you add them together, you get 130 degrees plus 50
degrees, which is 180 degrees. So they are supplementary. So let me write that down. Angle DBA and angle
ABC are supplementary. They add up to 180 degrees. But they are also
adjacent angles. And because they're
supplementary and they're adjacent, if you
look at the broader angle, the angle used from the sides
that they don't have in common. If you look at
angle DBC, this is going to be essentially
a straight line, which we can call a straight angle. So I introduced you to
a bunch of words here. And now I think we have
all of the tools we need to start doing
some interesting proofs. And just to review here,
we talked about any angles that add up to 90 degrees are
considered to be complementary. This is adding up to 90 degrees. If they happen to be adjacent,
then the two outside sides will form a right angle. When you have a right angle,
the two sides of a right angle are considered to
be perpendicular. And then if you have two angles
that add up to 180 degrees, they're considered
supplementary. And then if they
happen to be adjacent, they will form a straight angle. Or another way, if you said,
if you have a straight angle and you have one of the
angles, the other angle is going to be
supplementary to it. They're going to add
up to 180 degrees. So I'll leave you there.