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## Geometry (all content)

### Course: Geometry (all content)>Unit 2

Lesson 7: Angles between intersecting lines

# Missing angles with a transversal

When a third line called a transversal crosses two parallel lines, we can find the measures of angles using properties like corresponding angles, vertical angles, and supplementary angles. If we know just one of the angle measurements, these properties help us find all the missing angle measurements. Created by Sal Khan.

## Want to join the conversation?

• can transversal line be perpendicular to parallel lines?
• Yes it can, it crosses through two lines at a certain point, so I would consider it transversal. It would create perpendicular lines.
• all of you are super smart
do your dreams i know you can do it.
• What is a congruent angle?
• Congruent angles are, by definition, angles that have the same degree measure.
• How do you remember the difference between supplementary and complementary?
• 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

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!
• How would I know if the lines are parallel? Therefore how would I know it actually is a transversal
• 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.
• How did he find out what the pink angle was?
• 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!
• 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)
• "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"
• 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?
• Two angles that sum to a complete circle (1 turn, 360°) are called explementary angles or conjugate angles.
• Pretty good thanks for asking :)
• Can a transversal or however you say it be perpendicular?... To parallel lines?
• There is something called a perpendicular transversal, so yes.

## 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.