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Equation practice with complementary angles

Given the algebraic expressions that represent a pair of complementary angles, learn how to form and solve an equation to find an unknown angle. Created by Sal Khan.

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  • aqualine seed style avatar for user prlmcfadden92
    how did you get 90
    (2 votes)
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  • aqualine ultimate style avatar for user Amanda Mcdermott
    after 1.30 i got lost. i have no clue how he finished this equation. Specifically the part where he found out what x was.
    (2 votes)
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  • starky ultimate style avatar for user SouthDakotaGirl
    At , How do i know whether I should Add or subtract?
    (6 votes)
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    • male robot hal style avatar for user John Malig
      We want to solve for x, and that means we need to isolate x on one side of the equation. Since we have 5x+40 = 90, in order to just have x on the left-hand side, we would need to get rid of the 5 and +40. First, +40. To get rid of it and make it 0, what do we need to do? Well, we need to subtract 40 since 40-40 = 0. But if we only did that to one side, the equation wouldn't hold up anymore. So, we subtract 40 from 90: 90-40 = 50. So, we have 5x = 50. And the left-hand side is still multiplying x by 5, so what do we need to do to get rid of that 5? Well, the opposite of multiplication is division. So, we divide by 5. 5 times x divided by 5 = x. But we also need to do the same operation to the other side. So, 50 divided by 5 = 10. And so we're left with x = 10.
      (13 votes)
  • duskpin tree style avatar for user Seneth
    Is ray the same thing as line?
    (2 votes)
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    • piceratops seedling style avatar for user Asha
      No, a ray is a like a line segment, and an arrow so it's basically an arrow on one end of a line and a dot on the other Ex. •-->

      A line segment is a line with two dots on the sides. Ex. •--•

      A line is a straight line that has arrows on the side. Ex. <---> Hope I helped you!
      (8 votes)
  • piceratops seedling style avatar for user CONNORR
    I might be a bit slow or dumb but i don't understand anything after 2x + 46 + 3x - 6 = 90 can you explain please.
    (4 votes)
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    • duskpin ultimate style avatar for user Neal
      x in this case is a variable, and it could be any number, even a negative number or a repeating decimal like 2.334334...
      So first we have 2x + 46 + 3x - 6 = 90
      We add the Xs and the numbers on the left hand side to get
      5x + 40 = 90
      We subtract 40 from both sides to get
      5x = 50
      Finally, we divide both sides by 5
      x = 10
      Hope this helps
      (2 votes)
  • male robot johnny style avatar for user Patrick
    how does this work I am so confused?
    (3 votes)
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    • hopper cool style avatar for user Stanley Z.
      Complementary angles are where the sum of two or more angles add up to 90 degrees. So all you do is add all the angles together equal 90 degrees. If the angles are in the form of an expression (like this video), then add all the expressions together equal to 90, solve for the variable and then plug it back into the expressions to find the measure of the angles. Hope that makes it clear.
      (2 votes)
  • starky tree style avatar for user Amber Chen
    How did you gonna know which angle is 90 or the number
    (2 votes)
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  • blobby green style avatar for user jordan.pankey
    given m<qps=40 degrees what will be the meausure of qrp
    (1 vote)
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  • aqualine ultimate style avatar for user Gray Grimm
    Did you mean 34 at the end of the video? Because last time I checked 3x10 is 30 and then subtract the 6... ?
    (2 votes)
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  • starky tree style avatar for user Kai
    How would you do this if you don't know what the total angle is?
    (2 votes)
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Video transcript

So we're told that ray OL is perpendicular to ray ON. So OL is perpendicular to ON. So we know that this right over here is a right angle, or it's a 90-degree angle. Then they tell us that the measure of angle LOM is equal to 2x plus 46. So LOM-- so this angle right over here-- is equal to 2x plus 46. Then they tell us that the measure of angle MON is equal to 3x minus 6. So this angle right over here is 3x minus 6. And so they ask us find angle MON. So we need to find this angle right over here. And we'd be able to find it if we knew what x is. If we knew what x is, then it's going to be 3 times that minus 6. Now, the one thing that we know is that if we add up these two angles, these are adjacent angles. And their outside rays form a right angle. So these two angles are going to add up to 90 degrees. And I guess we can assume here that we're dealing in degrees. So let's say that 2x plus 46 plus 3x minus 6 is going to add up to 90 degrees. These two angles are complementary. So it's going to add up to 90 degrees, or it's going to add up to 90. And now, we just have to simplify. We have 2 x's. We have another 3 x's. So you add those two, and you're going to get 5 x's. And then you have 46. And you're going to subtract 6. So it's going to be plus 40 is equal to 90. Subtract 40 from both sides. So let's do that. Subtract 40 from both sides. And on the left-hand side, you're just left with a 5x. And on the right-hand side, you're left with a 50. Now, just divide both sides by 5. And we are left with x is equal to 10. Now, our answer is not 10. We've just figured out what x is. What they ask us for is what's the measure of angle MON? Well, we already know that the measure of angle MON is equal to 3x minus 6, which is equal to 3 times 10 minus 6-- I want to do that minus 6 in that green color-- which is equal to 24 degrees.