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Equation practice with vertical angles

Given algebraic expressions that represent a pair of vertical angles, Sal forms and solves an equation. Created by Sal Khan.

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  • blobby green style avatar for user Katie Smith
    Are vertical angles complementary or supplementary or does it depend on the degrees in the question?
    (2 votes)
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    • primosaur ultimate style avatar for user Nicholas Beirne
      Vertical angles are basically another word for opposite angles. If one of the vertical angles is 90° then the other one has to be 90° This would make it supplementary, because if both of the angles are 90 degrees they add up to 180°. The same thing goes for the complementary angles, because there is only one way to represent them. Since vertical angles have the same measure on their mirrored side, there is no other way to make 90° aside from 45° and 45°. This meaning that 31° and 59° degrees would not work. ( This is the same for the supplementary angles ) So yes, the vertical angles could either be supplementary, complementary, or something else ( such as 67° and 67° are vertical angles, yet they are not supplementary or complementary because they don't add up to either 90° or 180°. So your answer could be yes, meaning that they could be both, but your answer also could be no, because there are many different ways, such as my example, which adds up to 134°, meaning that it is not supplementary or complementary. Hopefully you found this useful (also sorry if it was too long)
      (2 votes)
  • spunky sam red style avatar for user 🏮🔥Phoenix Warrior🔥🏮
    Is it just me or does it seem that everybody's post gets a vote as soon as you post it?
    (5 votes)
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  • hopper cool style avatar for user Shiv Sah👨‍🚀🚀🌕
    Hey fellows, does it matter if we put 7x+182 at first and 9x+194 at last?

    Like this----- 7x+182 = 9x+194
    (5 votes)
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  • blobby green style avatar for user Linda Ligonde
    when setting up the equation, does it matter which piece goes first? Because sometimes I would do the problem, and it would come out the opposite of the correct answer.
    (4 votes)
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  • primosaur ultimate style avatar for user khanballer
    Can you give me a summary of this video vertical angles is a very ambiguous concept.
    (2 votes)
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    • hopper happy style avatar for user Genius
      In this lesson the vertical angles part isn't important. Sal uses vertical angles as an application of a question like the ones he demonstrated in the video. Here is an example:

      9x+72=4x+112
      (9x+72)-4x=(4x+112)-4x
      5x+72=112
      Here we will "switch" the numbers around and combine like terms
      5x=112-72
      5x=40
      x=8 degrees
      Hope this helps.
      (2 votes)
  • hopper cool style avatar for user ♛TooGoodAtFPS♛
    you said that the angle measurement is 140 degrees but the angle is acute
    (4 votes)
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  • blobby green style avatar for user Omi
    9x+194=7x+182
    9x-7x=182-194
    2x = -12
    x = -12 divided by 2
    x = -6
    I calculated like this. Is that be helpful?
    (2 votes)
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  • blobby green style avatar for user casper907.cp
    What if their is a vertical angle. But one is 3x and the other is (80-x)? How would you solve that?
    (2 votes)
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    • leaf orange style avatar for user †Great_Gabe†
      If the angles are vertical, then they are congruent, or the same measure. Therefore, if a vertical equals 3x and the other equals 80-x, you would simply set up an equation: 3x equals 80-x. add x to both sides, then you would get 4x equals 80. Solve for x, and you get x equals 20. I hope this helps you!
      (2 votes)
  • starky ultimate style avatar for user Alexis West
    Do all vertical angles equal 360 degrees?
    (2 votes)
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  • duskpin sapling style avatar for user Stephen Cola
    how can both of those angles be 140 degrees when they are both acute angles?
    (2 votes)
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Video transcript

Let's say we have two intersecting lines. So that's one of the lines right over there. And then I have another line right over here. So those are my two intersecting lines. And let's say we know that the measure of this angle right over here is equal to 7x plus 182. And this is being given in degrees, so it's 7x plus 182 degrees. And we know that the measure of this angle right over here is 9x plus 194 degrees. So my question to you is, what is the measure of each of these angles? And I encourage you to pause the video and to think about it. Well, the thing that might jump out at you is that these two things are vertical angles. They're the opposite angles when we have these intersecting lines right over here. And vertical angles are equal to each other. So we know, because these are vertical angles, that 9x plus 194 degrees must be equal to 7x plus 182 degrees. And now we just have to solve for x. So if we want all the x-terms on the left-hand side, we could subtract 7x from here. We've got to do it to both sides, of course, in order to maintain the equality. And then we could put all of our constant terms on the right-hand side. So we can subtract 194 from the left. We have to subtract 194 from the right in order to maintain the inequality. And on the left, what we're left with is just 2x. And on the right, what we're left with-- let's see. 182 minus 194. So if it was 194 minus 182, it would be positive 12. But now it's going to be negative 12. We're subtracting the larger from the smaller, so it's equal to negative 12. And then divide both sides by 2. And we get x is equal to negative 6. And now we can use that information to find out the measure of either one of these angles, which is the same as the other one. So we can see here that if we take 7 times negative 6 plus 182, so 7 times negative 6 is negative 42, plus 182 is going to be equal to 140 degrees. And you'll see the same thing over here. If we say 9 times negative 6, which is negative 54, plus 194, this also equals 140 degrees.