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Vertical angles

By using our knowledge of supplementary, adjacent, and vertical angles, we can solve problems involving the intersection of two lines. Including this one! Created by Sal Khan.

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  • leaf green style avatar for user butterflies
    What is the difference between intercept and intersecting? anyone?
    (110 votes)
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    • mr pants teal style avatar for user Willa Lovette
      Intercept and intersect are similar terms used in different math subjects. An intercept, as in x or y intercept, is a term commonly used in graphing, where a line crosses your y or x axis at zero. An intersection is used in geometry, where a line segment or a ray crosses another. Hope this helped!
      (172 votes)
  • blobby green style avatar for user shitanshuonline
    How is CEF adjacent () ?
    (18 votes)
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  • duskpin ultimate style avatar for user Hamad Chughtai
    What are adjacent, supplementary and complimentary angles? anyone?
    (10 votes)
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  • blobby green style avatar for user samdasika
    This is hard. Idu.-I don't understand. Can someone explain me?
    (1 vote)
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    • female robot grace style avatar for user Gracy
      In supplementary angles the sum of 2 angles should be equal to 180
      For example.... 60°+120° =180°
      70°+110°=180°
      AND SO ON

      in this question the angle <BED = 70° which is already given

      To find the measure of BEC
      which can be take out very easily as both angles are supplementary so we can find it by

      70°+_____=180°
      Which is equal to 110°


      And the angles which are in front of each other are always equal

      Hope it helps🥰

      Thank you


      Please vote if It helps ..........
      (50 votes)
  • hopper jumping style avatar for user :)
    Can angles be complementary and/or supplementary without being adjacent? Thx in advance
    (14 votes)
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    • mr pink green style avatar for user David Severin
      Yes if you have two parallel lines and a transversal, there are all sorts of supplementary angles (same side interior, same side exterior) that are not adjacent. In a right triangle, the two acute angles will always be complementary. They do not have to even be related to each other in any way, they can be drawn independently.
      (11 votes)
  • male robot hal style avatar for user Jordan Holmes
    I'm very confused about the whole thing. Can you please help me understand it a little bit more? That would be nice if you could do that for me. Thank you for time to help me understand even though I watched to video.

    - Jordan Holmes
    (8 votes)
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    • piceratops ultimate style avatar for user Daniel
      Hi Jordan.
      I'm not sure which part of the video you need help with, so I'll go through each section.
      Okay, let's start!

      @ So we can see that the angles BED and CEB are adjacent. This means that they are next to each other. Also, we know that the line CED is straight. This is important, so remember it!
      @ By supplementary, Sal means that they both add up to 180 degrees. So angle BED is 70 degrees, and both angles add up to 180 degrees, so we can safely say that angle CEB is 110 degrees.
      @ Alright. So we know that angle CEB is 110 degrees. So what about angle CEA? Well, we know that the two angles are adjacent. And we also know that line AEB is straight. So again, we can conclude that angles CEB and CEA are supplementary. So, 180-110=70! Hmm! That number looks familiar! It seems that angles CEA and BED are the same! We'll talk about this in the next section.
      @ Because the angles are opposite each other in this diagram, they are called "vertical angles" Vertical angles are the same. So, as we can see, angles CEA and BED are vertical!
      @ By applying this same rule, we see that angles CEB and AED are vertical too. So we can comfortably say that angle AED is 110 degrees. And to confirm, we can see that angles CEA and AED are supplementary, and so 180-70=110
      @ Finally, we can see that every semicircle adds up to 180 degrees, while every full circle adds up to 360 degrees. Also, every quarter circle adds up to 90 degrees.

      Okay! I hope that sums up the video nicely! If you have any questions, feel free to ask them in the comments and I'll reply ASAP. Thanks for reading!
      - Daniel
      (17 votes)
  • blobby green style avatar for user designsbyharp
    How are angles:CEA and CEB Adjacent? They aren't connecting to one line..
    (9 votes)
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    • starky sapling style avatar for user Dayla
      The angles CEA and CEB are indeed adjacent. As you can see by looking at the letters they have both C and E. Both angles share a common vertex of E and they also share the line segment of C, therefore, they are touching, or adjacent.
      (7 votes)
  • blobby green style avatar for user Yasir Bhura
    So what is exactly a vertical angle?
    (4 votes)
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  • duskpin ultimate style avatar for user yuchunxu2015
    Are there any tricks to remember complimentary, vertical, and supplementary angles?
    (6 votes)
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    • mr pink green style avatar for user David Severin
      complimentary and supplementary are not quite related to vertical, so you should not put all three together. Vertical angles are across from each other on any two intersecting lines and are always congruent.
      If you draw a line across the C, it sort of looks like a 9, so it is two angles adding to be 90, If you draw a line across the S, it sort of looks like an 8 to remind us that it is two angles adding up to 180.
      (4 votes)
  • starky sapling style avatar for user Doyeon Yun
    What if an angle is 0 degrees. Will the angle be 180 degrees because it will pretty much be a line like ______
    (6 votes)
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Video transcript

Let's say I have two intersecting line segments. So let's call that segment AB. And then I have segment CD. So that is C and that is D. And they intersect right over here at point E. And let's say we know, we're given, that this angle right over here, that the measure of angle-- That B is kind of, I don't know why I wrote it so far away. So let me make that a little bit closer. Let me make that B a little bit closer. So let's say-- I'll do that in yellow. Let's say that we know that the measure of this angle right over here, angle BED, let's say that we know that measure is 70 degrees. Given that information, what I want to do, based only on what we know so far and not using a protractor, what I want to do is figure out what the other angles in this picture are. So what's the measure of angle CEB, the measure of angle AEC, and the measure of angle AED? So the first thing that you might notice when you look at this, I've already told you that this is a line segment and that this is a line segment. You see that angle BED and angle CEB are adjacent. And we also see that if you take the outer sides of those angles, it forms a straight angle. And we also see that angle CED is a straight angle. So we know that these two angles must also be supplementary. They're next to each other and they form a straight angle when you take their outer sides. So we know that angle BED and angle CEB are supplementary, which means they add up to, or that their measures add up to 180 degrees. Supplementary angles. Which tells us that the measure of angle BED plus the measure of angle CEB-- and I keep writing measure here. Sometimes you'll just see people write, angle BED plus angle CEB is equal to 180 degrees. Now we already know the measure of angle BED is 70 degrees. So we already know that this thing right over here is 70 degrees. And so 70 degrees plus the measure of angle CEB is 180 degrees. You subtract 70 from both sides, and we get the measure of angle CEB is equal to 110 degrees. I just subtracted 70 from both sides of that. So we figured out that this right over here is 110 degrees. Well, that's interesting. And I went through more steps than you would if you were doing this problem quickly. If you did this problem quickly in your head, you'd say, look this is 70 degrees, this angle plus this angle would be 180 degrees, so this has to be 110 degrees. So now let's use the same logic to figure out what angle CEA is. So now we care about the measure of angle CEA. And we can use the exact same logic that we used over here. Angle CEA and angle CEB, they are adjacent. They form a straight angle, if you look at their outsides, so they must be supplementary. They form a straight angle right over here. So they're supplementary. So they must add up to 180 degrees. So the measure of angle CEA plus the measure of angle CEB, which is 110 degrees, must be equal to 180 degrees. So once again, subtract 110 from both sides. You get the measure of angle CEA is equal to 70 degrees. So this one right over here is also 70 degrees. And what we'll learn in the next video is that this is no coincidence. These two angles, angle CEA and angle BED, sometimes they're called opposite angles-- well, I have often called them opposite angles, but the more correct term for them is vertical angles. And we haven't proved it. We've just seen a special case here where these vertical angles are equal. But it actually turns out that vertical angles are always equal. But we haven't proved it to ourselves for the general case. But let me just write down this word since it's a nice new word. So angle CEA and angle BED are vertical. And you might say, wait, they look like they're horizontal, they're next to each other. And the vertical really just means that they're across from each other, across an intersection from each other. Angle CEB and angle AED are also vertical. So let me write that down. Angle CEB and angle AED are also vertical. And that might even make a little bit more sense, because it literally is, one is on top and one is on bottom. They're kind of vertically opposite from each other. But these horizontally opposite angles are also called vertical angles. So now we have one angle left to figure out, angle AED. And based on what I already told you, vertical angles tend to be, or they are always, equal. But we haven't proven that to ourselves yet so we can't just use that property to say that this is 110 degrees. So what we're going to do is use the exact same logic. CEA and AED are clearly supplementary. Their outsides form a straight angle. They're clearly supplementary, so CEA and AED must add up to 180 degrees. Or we could say the measure of angle AED plus the measure of angle CEA must be equal to 180 degrees. We know the measure of CEA is 70 degrees. We know it is 70 degrees. So you subtract 70 from both sides. You get the measure of angle AED is equal to 110 degrees. So we got the exact result that we expected. So this angle right over here is 110 degrees. And so if you take any of the adjacent angles that their outer sides form a straight angle, you see they add up to 180. This one and that one add up to 180. This one and that one add up to 180. This one and that one add up to 180. And this one and that one add up to 180. If you go all the way around the circle, you'll see that they add up to 360 degrees. Because you literally are going all the way around. So 70 plus 110 is 180, plus 70 is 250, plus 110 is 360 degrees. I'll leave you there. This is the first time that we've kind of found some interesting results using the tool kit that we've built up so far. In the next video, we'll actually prove to ourselves using pretty much the exact same logic here, but we'll just do it with generalized numbers-- we won't use 70 degrees-- to prove that the measure of vertical angles are equal.