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## 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)

- 0:00Let's say I have an angle ABC, and it0:03looks something like this.0:05So its vertex is going to be at B. Maybe0:09A sits right over here, and C sits right over there.0:14And then also let's say that we have another angle called DBA.0:22I want to have the vertex once again at B. So let's0:26say it looks like this.0:27So this right over here is our point D. That is our point D.0:33And let's say that we know that the measure of angle DBA0:39is equal to 40 degrees.0:41So this angle right over here, its measure0:43is equal to 40 degrees.0:45And let's say that we know that the measure of angle ABC0:50is equal to 50 degrees.0:55So there's a bunch of interesting things happening0:57here.0:58The first interesting thing that you might realize1:00is that both of these angles share a side.1:03If you view these as rays-- they could be lines, line segments,1:06or rays-- but if you view them as rays,1:08they both share this ray BA.1:11And when you have two angles like this1:13that share the same side, these are called adjacent angles.1:16Because the word "adjacent" literally means next to.1:21These are adjacent.1:23They are adjacent angles.1:26Now there's something else that you1:27might notice that's interesting here.1:29We know that the measure of angle DBA is 40 degrees1:32and the measure of angle ABC is 50 degrees.1:35And you might be able to guess what the measure of angle DBC1:40is.1:44If we drew a protractor over here--1:46I'm not going to draw it.1:47It will make my drawing all messy.1:49Well, maybe I'll draw it really fast.1:51So if you had a protractor right over here,1:52clearly this is opening up to 50 degrees.1:55And this is going another 40 degrees.1:57So if you wanted to say what the measure of angle DBC is,2:01it would essentially be the sum of 40 degrees and 50 degrees.2:04And let me delete all of this stuff2:06right here to keep things clean.2:07So the measure of angle DBC would be equal to 90 degrees.2:13And we already know that 90 degrees is a special angle.2:16This is a right angle.2:22There's also a word for two angles whose sum add up2:26to 90 degrees, and that is complementary.2:30So we can also say that angles DBA and angles2:38ABC are complementary.2:46And that is because their measures add up to 90 degrees.2:50So the measure of angle DBA plus the measure of angle ABC2:57is equal to 90 degrees.3:00They form a right angle when you add them up.3:03And just as another point of terminology3:05that's kind of related to right angles,3:09when a right angle is formed, the two rays3:12that form the right angle or the two lines that3:14form that right angle or the two line segments that3:17form that right angle are called perpendicular.3:19So because we know that measure of angle DBC is 90 degrees3:23or that angle DBC is a right angle, this tells us,3:28we know that the line segment DB is3:36perpendicular to line segment BC.3:46Or we could even say ray BD is-- instead of using the word3:53perpendicular, there's sometimes this symbol3:55right here, which really just shows two perpendicular3:58lines-- perpendicular to BC.4:02So all of these are true statements here.4:06And these come out of the fact that the angle4:08formed between DB and BC, that is a 90-degree angle.4:14Now, we have other words when our two angles add up4:17to other things.4:19So let's say, for example, I have one angle over here.4:31Let me put some letters here so we can specify it.4:33So let's say this is X, Y, and Z.4:37And let's say that the measure of angle XYZ4:40is equal to 60 degrees.4:45And let's say that you have another angle that4:48looks like this.4:52And I'll call this, let's say, maybe MNO.

•Current transcript segment:5:02And let's say that the measure of angle MNO is 120 degrees.5:07So if you were to add the two measures of these-- so let5:10me write this down.5:11The measure of angle MNO plus the measure of angle XYZ,5:25this is going to be equal to 120 degrees plus 60 degrees, which5:30is equal to 180 degrees.5:32So if you add these two things up,5:35you essentially are able to go all halfway around the circle.5:38Or you could go throughout the entire half circle5:41or semicircle for a protractor.5:43And when you have two angles that add up to 180 degrees,5:47we call them supplementary.5:49I know it's a little hard to remember sometimes.5:5190 degrees is complementary.5:52They're just complementing each other.5:54And then if you add up to 180 degrees,5:56you have supplementary.5:58You have supplementary angles.6:03And if you have two supplementary angles that6:05are adjacent so that they share a common side-- so let6:08me draw that over here.6:10So let's say you have one angle that looks like this.6:13And that you have another angle.6:15So let me put some letters here again.6:18And I'll start reusing letters.6:19So let's say that this is ABC.6:23And you have another angle that looks like this.6:31I already used C.6:36Once again, let's say that this is 50 degrees.6:39And let's say that this right over here is 130 degrees.6:42Clearly, angle DBA plus angle ABC, if you add them together,6:49you get 130 degrees plus 50 degrees, which is 180 degrees.6:52So they are supplementary.6:53So let me write that down.6:55Angle DBA and angle ABC are supplementary.7:04They add up to 180 degrees.7:07But they are also adjacent angles.7:14And because they're supplementary7:16and they're adjacent, if you look at the broader angle,7:19the angle used from the sides that they don't have in common.7:22If you look at angle DBC, this is7:29going to be essentially a straight line, which7:31we can call a straight angle.7:37So I introduced you to a bunch of words here.7:39And now I think we have all of the tools we7:41need to start doing some interesting proofs.7:45And just to review here, we talked about any angles7:50that add up to 90 degrees are considered to be complementary.7:55This is adding up to 90 degrees.7:56If they happen to be adjacent, then the two outside sides8:00will form a right angle.8:03When you have a right angle, the two sides of a right angle8:06are considered to be perpendicular.8:09And then if you have two angles that add up to 180 degrees,8:12they're considered supplementary.8:14And then if they happen to be adjacent,8:16they will form a straight angle.8:18Or another way, if you said, if you have a straight angle8:21and you have one of the angles, the other angle8:24is going to be supplementary to it.8:26They're going to add up to 180 degrees.8:28So I'll leave you there.(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.