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## 8th grade (Eureka Math/EngageNY)

### Unit 2: Lesson 3

Topic C: Congruence and angle relationships- Congruence and similarity — Basic example
- Congruence and similarity — Harder example
- Angles, parallel lines, & transversals
- Parallel & perpendicular lines
- Missing angles with a transversal
- Angle relationships with parallel lines
- Measures of angles formed by a transversal
- Equation practice with angles
- Angles in a triangle sum to 180° proof
- Triangle exterior angle example
- Find angles in triangles
- Find angles in isosceles triangles
- Worked example: Triangle angles (intersecting lines)
- Worked example: Triangle angles (diagram)
- Finding angle measures between intersecting lines
- Finding angle measures using triangles
- Triangle angle challenge problem
- Triangle angle challenge problem 2

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# Missing angles with a transversal

CCSS.Math:

Learn how to find missing angle measurements in a figure with two parallel lines and a transversal. Created by Sal Khan.

## Want to join the conversation?

- can transversal line be perpendicular to parallel lines?(22 votes)
- Yes it can, it crosses through two lines at a certain point, so I would consider it transversal. It would create perpendicular lines.(9 votes)

- What is a congruent angle?(14 votes)
- Congruent angles are, by definition, angles that have the same degree measure.(30 votes)

- all of you are super smart

do your dreams i know you can do it.(27 votes) - How do you remember the difference between supplementary and complementary?(9 votes)
- Remember:
**Complementary angles**add up to 90°

-*example: 20° & 70°*

(added together, they form a right angle)

-and-**Supplementary angles**add up to 180°

-*example: 60° & 120°*

(added together, they form a straight line)**Two facts**:

(1) 90° comes before 180° on the number line

(2) "C" comes before "S" in the alphabet

You can use this to help you remember!

90° goes with "C" for complementary*so complementary angles add up to 90°*

180° goes with "S" for supplementary*so supplementary angles add up to 180°*

Hope this helps!(27 votes)

- How would I know if the lines are parallel? Therefore how would I know it actually is a transversal(8 votes)
- Bvanplane,

Either it has to be given that the lines are parallel,

Or you have to be given two angles that allow you to determine that like angles are equal,

Or you could be given an equation for the lines like

2x+3y=2 and

2x+3y = 8 which lines would have no solution, therefore they do not cross, therefore they are parallel.(18 votes)

- How did he find out what the pink angle was?(5 votes)
- The line where the transversal intercepts one of the parallel lines create 180 degrees due to the rule of supplementary angles. Supplementary is when two or more angles add up to 180 degrees. So Mr. Khan knew that the one measurement was 110 degrees. Using the rule of Supplementary angles, you know that the other side of the line must be 70 degrees, since 110 + 70 = 180. I hope you find this helpful!(2 votes)

- Why was "x" invented for math?!

(2 year later edit: Hi now that im in 6th i understand x and different kind of variables i was just too young to understand)(4 votes)- "x" was invented as a variable to replace unknown numbers. So if I had 10 cookies in a jar and ate 3, (I know the answer is obvious) but say I didn't know how many are left. I could use x instead of a question mark. So 10 - 3 = x

Variables are also helpful because if I had two unknown numbers that were different in value, I could use x and y, instead of using the same ? for different values.

(x) is very helpful in life and I first learned about it in Pre-Algebra.

I hope I helped you.

"You only need to know one thing, you can learn anything"(7 votes)

- If complementary angles add up to 90 degrees and supplementary angles add up to 180, are there terms for angles that add up to 270 degrees and 260 degrees?(0 votes)
- Two angles that sum to a complete circle (1 turn, 360°) are called explementary angles or conjugate angles.(4 votes)

- What does supplementary mean?(4 votes)
- Supplementary means that all the angles on a certain line add up to 180 degrees. Supplement means, by definition according to Oxford, "Completing or enhancing something." In context, the angles
**complete**each other to equal 180 degrees. They**enhance**each other.(2 votes)

- Can a transversal or however you say it be perpendicular?... To parallel lines?(3 votes)
- There is something called a perpendicular transversal, so yes.(5 votes)

## Video transcript

Let's say that we have
two parallel lines. So that's one line
right over there, and then this is
the other line that is parallel to the first one. I'll draw it as
parallel as I can. So these two lines are parallel. This is the symbol
right over here to show that these two
lines are parallel. And then let me draw
a transversal here. So let me draw a transversal. This is also a line. Now, let's say that we know
that this angle right over here is 110 degrees. What other angles can
we figure out here? Well, the first thing
that we might realize is that, look, corresponding
angles are equivalent. This angle, the angle
between this parallel line and the transversal,
is going to be the same as the angle
between this parallel line and the transversal. So this right over here is
also going to be 110 degrees. Now, we also know that
vertical angles are equivalent. So if this is 110
degrees, then this angle right over here on the opposite
side of the intersection is also going to be 110 degrees. And we could use that
same logic right over here to say that if this
is 110 degrees, then this is also 110 degrees. We could've also
said that, look, this angle right over here
corresponds to this angle right over here so that they
also will have to be the same. Now, what about
these other angles? So this angle right over
here, its outside ray, I guess you could
say, forms a line with this angle right over here. This pink angle is supplementary
to this 110 degree angle. So this pink angle plus 110
is going to be equal to 180. Or we know that this pink angle
is going to be 70 degrees. And then we know that it's a
vertical angle with this angle right over here, so
this is also 70 degrees. This angle that's kind of
right below this parallel line with the transversal, the bottom
left, I guess you could say, corresponds to this bottom
left angle right over here. So this is also 70 degrees. And we could've also
figured that out by saying, hey, this angle is supplementary
to this angle right over here. And then we could use
multiple arguments. The vertical angle argument,
the supplementary argument two ways, or the corresponding
angle argument to say that, hey, this must be
70 degrees as well.