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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 vertical angles

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

## Want to join the conversation?

- Can you give me a summary of this video vertical angles is a very ambiguous concept.(33 votes)
- 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.(37 votes)

- Are vertical angles complementary or supplementary or does it depend on the degrees in the question?(18 votes)
- 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)(10 votes)

- Is it just me or does it seem that everybody's post gets a vote as soon as you post it?(12 votes)
- What if their is a vertical angle. But one is 3x and the other is (80-x)? How would you solve that?(6 votes)
- 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!(7 votes)

- how do I know what to subtract off of? for example: Sal subtracted 7x off on both sides. does that mean you take the smaller of the numbers beside the x to subtract, or does that mean you just take the one on the right to subtract?(5 votes)
- He's constraining the variables by 'cancelling', using legitimate operations and following the addition rule of equalities. He happened to cancel 7x, but could have chosen anything else as long as it constrains the variable to the form variable = number. https://youtu.be/vA-55wZtLeE https://youtu.be/f15zA0PhSek(6 votes)

- On my worksheet, it has a problem that does not contain numbers. It is just two lines in a x shape, then y over 4, x, y, and y in each spot. Then it says to find out what x and y are. Pls help! I am in the 6th grade gifted program and in fast math, if that helps(2 votes)
- y and y are obviously vertical angles. That means that the remaining two angles: x and y/4 must be vertical angles. Therefore:

y = y (duh)

x = y/4 (little more helpful)

the first equation: y = y won't help us since we need a system with with two variables in each equation. Remember that angles on the same line are supplementary:

y + x = 180

Now we can solve the system:

x = y/4

y + x = 180

y + y/4 = 180

5y/4 = 180

5y = 520

y = 104deg

104 + x = 180

x = 76deg(5 votes)

- Can someone please assist me? I am having trouble making sense of this.(5 votes)
- Hello, but could you specify what you are confused about? I just need to know what is confusing you to help you.(0 votes)

- 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)
- 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)- Not at all, but the orientation of the angles has Sal's way a more logical choice.(0 votes)

- 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)

## 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.