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alternate exterior angles

Alternate Exterior angles sample problems.

two parallel lines  cut by transversal
Which of the following pairs of angles are alternate exterior angles if the two lines cut by the transversal are parallel?

A and F
A and E
E and F

answer alternate exterior angles
If angle E measures 60 degrees, what is the measure of angle B, if the two lines are parallel?

A. 120
B. Can't determine from information
answer 2 alternate exterior angles
Do alternate exterior angles have to be congruent? No they are congruent only when the lines being crossed are parallel.
Common Core Standard G.CO.9
Keywords: congruent angles, lines and angles,transversal,high school math

1. Alternate Exterior angles are located on opposite sides of the transversal, and are diagonal from one another.

2. They are outside the two lines. ( Outside the bun)​ In order to help visualize the difference between exterior and interior angles I think of a hamburger. See the picture below.

3. Alternate exterior angles are congruent. (equal angle measure) when the lines crossed by the transversal are parallel.

orange line

Alternate Exterior angles in real life

Check out these examples of alternate exterior angles in real life. Once you see these examples you will start to notice other examples all around you.
example from real life alternate exterior angle flag
parking lot real life example alternate exterior angle 1
alternate exterior angle real life example tennis racguet
car grill-alternate exterior angle
perpendicular transversal
Right Angle
hamburger illustrating alternate exterior angles
Common Core Standard G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Perpendicular Transversal


Interior Angles (inside the bun)

Exterior Angles (outside the bun)



Welcome to MooMooMath. Today we are going to look at alternate exterior angles. When do we have alternate exterior angles? You have them when you have two lines and a transversal crosses both of those lines. Sometimes those two lines are parallel and sometimes they aren’t. So we have line a and line b and we are going to say these two lines are parallel to each other. So we will mark them with these arrows that indicate that they are parallel. This line coming down the middle we will call line q and line q is the transversal. I like to think of this as a hamburger with the meat in between the two lines and the buns are where the alternate exterior angles will be found. Alternate means that it is found on opposite sides of the transversal. Then we have an external angle which means it is not between the two buns on the outside on the top and the bottom. Exterior is on the outside. So I will mark these in different colors. You have an alternate exterior angle here so I will call them angle 1 and angle 2 and they are your alternate exterior angles. Now I’m going to mark another angle. I’m going to mark 3 here and 4 here and those two angles are alternate exterior angles. Now there is something different about these angles. When you have two parallel lines and a transversal these alternate exterior angles are also congruent to each other and angles 1 and 3 are linear pairs so I’m going to throw out some numbers. Let’s say angle three is 50 degrees so we know angle 4 will also be 50 degrees because alternate exterior angles are congruent. Now we can also figure one and two since angle 3 is 50 and 1 and 3 are linear pairs and supplementary so I take 50 and subtract from 180 and that gives me 130 degrees. So angle 1 will be 130 degrees. So angle 2 down here will also be 130 degrees since they are alternate exterior angles and a linear pair with angle 4. So let’s look at the rules of alternate exterior angles. You have two lines that are parallel and we have a transversal so we know the alternate exterior angles have to be congruent to each other. What does it mean to be alternate exterior angles? Exterior means that you are on the outside and on opposite sides of the transversal. The alternate exterior angles are congruent if the lines are parallel. So that was a quick summary of alternate exterior angles.

orange line
orange line

Exterior Alternate Angles

q = Transversal
A  transversal is a line that cuts  across two or more lines.
Lines a and b
Parallel Lines
Angles 1 and 2 and Angles 3 and 4 Congruent Alternate Exterior Angles
Angles 1 and 3 and Angles 4 and 2 Supplementary Exterior Angles (180 degrees)

Alternate Exterior Angles

alternate exterior angles are congruent
alternate exterior angles

Definition of transversal

A transversal is a line that cuts across  two or more lines. If it crosses the two lines at a right angle it is a perpendicular transversal.
What are alternate exterior angles? When two lines are crossed by a transversal, the angle pair on the outside of the lines are alternate exterior angles. The two lines do not have to be parallel. A transversal is a line that cuts across two or more lines. Let's take a look at these angles.