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### Course: 8th grade (Illustrative Mathematics) > Unit 4

Lesson 5: Extra practice: Linear equations- Sums of consecutive integers
- Sums of consecutive integers
- Sum of integers challenge
- Equation practice with vertical angles
- Equation practice with vertical angles
- Equation practice with complementary angles
- Equation practice with supplementary angles
- Equation practice with angle addition

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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.

## Want to join the conversation?

- 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.(20 votes)
- Haha! Yes these videos can get confusing. He was trying to figure out what X was. To do that, you need to isolate it. First combine like terms (The ones with X, 2x and 3x, and the ones without X, 46 and -6.). That's how he got the equation 5x+40=90. Next you subtract 40 from both sides. Now you have 5x=50 (because 90-40 equals 50). To get rid of the 5, you divide it from both sides. You have X! x=10!(7 votes)

- how did you get 90(0 votes)
- how you know that it is a 90 degree is you will have the angle have a box at the part where it folds(8 votes)

- I might be a bit slow or dumb but i don't understand anything after 2x + 46 + 3x - 6 = 90 can you explain please.(9 votes)
- 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(8 votes)

- At1:40, How do i know whether I should Add or subtract?(5 votes)
- 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)

- Is ray the same thing as line?(3 votes)
- 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!(12 votes)

- Is anyone else confused by this? I mean like, yeah this is easy to most but i'm lost. Can i get help?(8 votes)
- just substitute complementary for "adds up to 90" and supplementary for " adds up to 180" in an equation. it should make sense then.(2 votes)

- What the heck is this(3 votes)
- Maybe this question is a little bit out of topic, but I am wondering:

We "denote" a ray with an arrow on top of the expression, but is this in any way related to vectors? (Vectors are beyond of what I've learned so far, but I've seen the notation multiple times in that context)(5 votes)- I guess they're related yeah. I've heard 3B1B refer to vectors as rays sometimes during his linear algebra series.

My understanding is that the definitions of these things differ a bit depending on the context/field. Mathematicians seem to prefer their vectors as rays that have one end stuck to the origin point (0, 0) on a plane. While physicists don't seem to distinguish between them and don't mind putting their vectors/rays anywhere they want, and that pisses off some mathematicians lol(3 votes)

- How did you gonna know which angle is 90 or the number(4 votes)
- Angles that are 90 degrees are marked with a little symbol that looks like the outer edges of a square, whenever you see that it means the angle is 90 degrees.(3 votes)

- 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)
- 30 minus 6 will be less than 30, so it's 24, not 34.(6 votes)

## 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.