# Vertical Angle Theorem

This video explains the vertical angle theorem. Learn about supplementary angles, adjacent angles, and linear pairs, plus bungee jumping. Intersecting lines have never been more fun.

 Geometry AnglesCongruence Language English Language Triangles Theorems About Triangles

### Transcript

00:25

If they both jump in opposite directions and don't hit each other… [The Thimbleton's bungee jump off a bridge]

00:30

…they'll make vertical angles.

00:32

If the angle the bungee cords make at the very top is 52 degrees…

00:37

…what angle will they make at the bottom?

00:40

To start, let's look at Mr. Thimbleton's bungee cord. [Mr. Thimbleton hanging down from the bridge]

00:45

Since it's a straight line, we know it makes a 180 degree angle.

00:49

That means our top angle plus this angle on the side make a linear pair…

00:54

…two angles that are supplementary and adjacent.

00:59

Since they’re supplementary, we know they add up to 180 degrees.

01:03

And because we know the top angle is 52 degrees, we can find the side angle by subtracting

01:09

180 minus 52.

01:12

The angle on the side is 128 degrees.

01:16

We're looking for the measure of the very bottom angle.

01:19

Let's consider Mrs. Thimbleton's bungee cord. [Mrs. Thimbleton hangs from the bridge]

01:23

It also makes a 180 degree angle, which means the side angle we just found and the bottom

01:28

angle also add up to 180 degrees.

01:31

If we take 180 minus 128, we end up with 52 degrees as the measure of the bottom angle.

01:39

Let's find the measure of the last angle. [Mr. Thimbleton pointing to the angle with his cane]

01:41

If we go through the same process and pick out a supplementary linear pair…

01:45

…we'll calculate 180 degrees minus 52 degrees equals 128 degrees.

01:51

So really, vertical angles are any two opposite angles formed by intersecting lines.

01:58

And the vertical angle theorem says that vertical angles are congruent… in other words, their [Mr. Thimbleton stood in front of a blackboard]

02:04

angles are equal.

02:05

Is this true?

02:07

Here we have two pairs of vertical angles:

02:09

The top and bottom, each measuring 52 degrees, and on the right and left, each measuring

02:15

128 degrees.

02:17

So yes.

02:18

Vertical angles, even if they're horizontal, are congruent.

02:22

Now you can be as secure with your knowledge of vertical angles as the Thimbletons are [The Thimbleton's jump off the bridge again and their dentures fall out]

02:27

to their huge bungee cords.