moomoomath logo header
lime green horizontal line
Welcome to MooMooMath
study skills A teachers secret guide to your best grades
Master the 7 pillars of school success

Improve your grades and lower your stress
A-Z Video List
Vertical angles are angles located across from each other. 
  • They also share the same vertex.  A vertex is a point where lines meet.
  • In addition vertical angles are congruent. (equal measure) 
  • An easy way to think of vertical angles is to visualize an X. An X would have two sets of vertical angles.

vertical angles

What is a Vertical Angle?

Transcript Vertical Angles
Hi Welcome to MooMooMath. Today we are going to talk about vertical angles. Vertical angles are angles that are across the street from each other, so you always look at vertical angles in relationship to each other. Notice, I have a line here, and I have a line here, and one here. I have one,two,three,four angles, so these are the angles I’m looking at, and the across the street neighbors are these two, and these two. If you will notice these two are smaller, and they are actually congruent to each other, which means they are equal measure. I’m going to mark these angles in blue with one little arc which shows they are congruent to each other. Then I’m going to mark these other angles congruent in green with two arcs and they are across from each other. These are what vertical angles are. These two blue angles are congruent, and these two green angles are congruent. Now I’m going to throw some numbers in there. What if I make this angle one hundred and twenty degrees how can I figure the rest. If this angle is one hundred and twenty degrees. We know this one has to be one hundred and twenty also because they are vertical angles. Now notice this is a straight line, and we know that lines add up to one hundred and eighty degrees. So if we have one twenty here we have sixty for the other side, so this vertical angle is also sixty degrees so that’s how vertical angles work. They are very simple once you get the hang of it. So let’s look at the rules of vertical angles. The rules are that angles across the street from each other are congruent, and that’s what a vertical angle is. Then angles adjacent from each other or next to each other are supplementary to each other or they add up to one eighty. Let’s look at our diagram. These two sixty degree angles are vertical angles, these two one twenty degree angles are vertical angles but these two next to each other are adjacent to each other and they add up to one eighty. Hope this was helpful. 

Angles and B are vertical angles and they are congruent ( equal angle measure)
 If angle A is 40 degrees then angle B is 40 degrees

Vertical angles in real life.

real life examples vertical angles snow skier
The skis crossing create vertical angles.
Vertical angles are found all around us. Here are just a couple examples. 
railroad crossing example vertical angles
Notice how the railroad crossing, and scissors create vertical angles.
real life example vertical angles scissors

Vertical angles sample problems

Find the angle measure for angles 1,2,and 3.
∠2 = 40◦ because it is a vertical of 40
40+40=80  Add the two vertical angles together
360-80= 280 because total measure = 360◦
280 ÷ 2 = 140◦
Angle 1 and 3 measure = 140◦  ∠1 and ∠3 are vertical angles 

another way to solve this problem is,
∠2 = 40◦ because it is a vertical of 40◦
∠2 and ∠3 are supplementary so 180-40 = 70◦
∠3  and ∠1 are vertical angles so ∠1  = 70◦

vertical angles
Find the value of X

     -12 =2x
​-6 = x
The two equations are equal because they are vertical angles.
Common Core Standard    6.CO.9