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## 7th grade (Eureka Math/EngageNY)

### Course: 7th grade (Eureka Math/EngageNY) > Unit 6

Lesson 1: Topic A: Unknown angles- Angles: introduction
- Name angles
- Complementary & supplementary angles
- Identifying supplementary, complementary, and vertical angles
- Complementary and supplementary angles (visual)
- Complementary and supplementary angles (no visual)
- Complementary and supplementary angles review
- Vertical angles
- Find measure of vertical angles
- Vertical angles
- Find measure of angles word problem
- Vertical angles review
- Finding missing angles
- Equation practice with supplementary angles
- Equation practice with complementary angles
- Create equations to solve for missing angles
- Unknown angle problems (with algebra)

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# Find measure of angles word problem

CCSS.Math:

Solve this word problem to find the measure of angles. In this example you'll split up a pie (don't forget to share!). Created by Sal Khan.

## Want to join the conversation?

- It seems like an equally valid answer would be that you cut yourself a 20 degree slice, and cut your brother a 10 degree slice. Where did the idea come from that these 3 slices would consume the entire remains of the pie?(80 votes)
- In fact, you're right. For it to be an exam question, it must be clearer.(30 votes)

- Couldn't you just do 180-30=150, then divide 150 by 3 which equals 50, and then multiply 50 times 2 to get 100? Wouldn't that be a lot simpler?(20 votes)
- yes but this strategy would only be valid with this specified problem(1 vote)

- I don't get any of this -_-(14 votes)
- Unfortunately, that is why we are here. to learn things like (9-4x) -2 (4y+8) +83y= -18x (14-13) -9x(2 votes)

- Two angles are supplementary. The measure of the larger angle is

10 degrees more than the product of 4 and the measure of the smaller angle.

What is the measure of the larger angle in degrees?(1 vote)- Let's call larger angle "x" and the smaller angle "y".

We can use the given information to create a system of equations:

x + y = 180 (this is because they are supplementary)

x = 4y + 10 (The measure of the larger angle is 10 degrees more than the product of 4 and the measure of the smaller angle.)

Solving this system:

4y + y + 10 = 180

5y + 10 = 180

5y = 170

y = 34˚

x + 34 = 180

x = 146˚(12 votes)

- Use an algebraic equation to find the measures of the two angles described below. Begin by letting x represent the degree measure of the angle's supplement.

The measure of the angle is nineteen times greater than its supplement.

what is the measure of the supplement?

can someone help me with this.(2 votes) - ok....this is a 4 min 33 sec video. when i found it out in less than a minut. half pie = 180 deg. mum slice so remaining 150. it will be 3x because little bro slice = x your slice equal to double so 2x. then x=150/3. x= 50. little bro slice = x so 50 ,yours 2x so 50*2 = 100. done(3 votes)
- First: mum slice? little bro slice? whaaat?

Second: Sal has to explain things in detail to make sure that EVERYONE gets what he's saying.(2 votes)

- can you help me with angle addition postulate(3 votes)
- The angle addition postulate states two angles that share a ray add up to make up a larger angle. This is useful to know because if you know two of the angles, you can figure out the third.

Example:

<ABC + <ABD= <CBD

<ABC=42

<CBD=87

87-42=45

You subtract 42 from 87 because you are removing one angle from the larger angle to find the other smaller angle.

I hope this helped!(1 vote)

- 180
*degrees*of a pie. Half of it is 90*degrees*. Now you have two parts of the whole 180*degrees*with each having 90*degrees*on each part.*30 degrees*is gone from one part of the 90*degrees*for your mom. (Imagine the 30*degrees*slice is a normal slice). You eat twice of what your brother eats so if your brother eats one slice (30*degrees*slice). Then that takes another slice of one of the 90*degrees*part. If your brother takes a 50 degrees slice of what's left of the pie. (30*degrees*plus 20*degrees*more) then your left with 100*degrees*for yourself which is twice more of your brothers piece of pie.**Did**I**do**anything**wrong**? Please inform me if I did.(2 votes) - A lot of people don't get this but this is the math: 1/2 pie /3 slices

1/2 pie = 180 degrees

your mom gets a 30 degree slice.

your brother gets half as much as you do so it would look like this`30+x(brothers slice)+2x(your slice) = 180`

3x(you and your brother's slices)+30(moms slice) = 180

Algebra tells you to isolate x so 3x = 150

isolate x even more and you get x=50 now thats your brothers slice, and multiplying it by 2 gets you 100 for your slice.

So this is your equation

50+100+30=180 perfect 150+30 does = 180!(2 votes) - how do you know your cuting to pie right(2 votes)

## Video transcript

There is a half
an apple pie left. You want to eat twice what
your little brother eats, but you also need to save
a slice for your mom. You can cut her a slice
that is 30 degrees. What is the measure of your
piece of the pie in degrees? So to tackle this, we just
have to remember a few things. We have to remember that
the degrees in a circle-- so if we were to go all
the way around a circle that that would be 360 degrees. But we only have
half a pie here. And actually, let me draw
a little bit differently. So if we had a whole pie--
so if we started here, and we had a whole pie, we
went all the way around, that would be 360 degrees. But we only have a half pie. So we only have 180 degrees
and let me do that in a color you're more likely to see. That's hard to see as well. We only have 180
degrees of pie left, but let's just keep
that in mind and think about how we're going to
split it between ourselves, our brother, and our mom. So let's define some variables. Let's let x be equal to the
degree measure of my brother's pie or your little
brother's pie. So this is degree
measure of brother's pie. And then what would the
amount of pie you eat be? Well, it says you eat twice
what your little brother eats. So 2x would be equal what
you eat, and it's really the degree measure
of what you eat. And then how much
does your mom eat? Well, it says you cut her
slice that is 30 degrees. So your mom's going to get
a 30 degree slice, going to get a slice of
something like that. So the amount that
your brother eats, x, plus the amount that you eat,
plus the amount that your mom gets, plus 30 degrees, is going
to be equal to this half pie. And remember, all of
these are degree measures. So it's going to be
equal to 180 degrees. And just to visualize
it over here, let me draw it down here
where it's easier to see it. We have half a pie that
we're dealing with. We're going to save 30
degrees for our mom. So that's 30 degrees
right over there. Your brother is going
to eat some amount. So that is x. And then you're going to
eat twice that amount. So that is 2x. x is the
measure of this angle, and then 2x is a
measure of that angle. So you see that 30
degrees plus x plus 2x, or x plus 2x plus
30 degrees, is going to be equal to 180 degrees. Now, we can simplify this. If we have one of something and
then have another two of it, how much do we have now? Well, I now have three x's. So 1x plus 2x is going to be 3x. So I have 3x plus 30 degrees
is going to be equal to, of course, 180 degrees. Now, to solve for x, we
can subtract 30 degrees from both sides. So minus 30 degrees,
minus 30 degrees. And I could have just written--
I could have all assumed that I'm doing it in degrees and
then just done it at the end. I keep writing it so I'll
just keep going with that. And then we are left
with 3x equaling 180 degrees minus 30 degrees
is equal to 150 degrees. And now we can just
divide both sides by 3, and we're left with x equaling
150 divided by 3 is 50 degrees. x is equal to 50 degrees. Now, we have to be careful. x is not what
they're asking for. They're asking for the
measure of your piece of pie in degrees. x is the degree measure of
your brother's piece of pie. What you eat is 2 times that. So if x is 50
degrees, 2 times that is going to be 100 degrees. So what is the measure of your
piece of the pie in degrees? It is going to be 100 degrees. So if we draw our pie again,
if we draw our half pie, you have 30 degrees
for your mom. So that's 30 degrees
for your mom. You have 50 degrees
for your brother. And then you have twice that
for yourself, 100 degrees.