Corresponding exterior angles

To begin with let's discuss the general characteristics of alternate angles:

Alternate angles between parallel lines are equal.
They are called alternate angles due to the fact that they:
• Are not on the same side of the transversal line
• Are not on the same "level" relative to the line

Here is an example of alternate angles:

Given that the two marked angles are not on the same level nor are they on the same side, they can be considered as alternate angles.
In order to understand what exterior alternate angles are, you must observe that:
There is the exterior part - outside the two parallel lines
As well as an interior part - between the two parallel lines.
Let's examine the illustration:

In the illustration, we observe that the two alternate angles located outside the two parallel lines are exterior alternate angles.

Let's look at another example of alternate exterior angles:

In this illustration both alternate angles are once again located in the external part and therefore they can be considered to be exterior alternate angles.

Bonus tip!
Alternate angles located in the inner part between two parallel lines are called alternate interior angles.

Now let's practice!
Here are two parallel lines and a line intersecting them.
a. Determine whether the angles shown are alternate angles.
b. Determine whether they are also alternate exterior angles.

Solution:
a. Yes, the angles in the figure are alternate angles. They are not on the same side of the transversal and not on the same level.
b. Yes, the alternate angles in the figure are exterior since they are located in the external part outside the two parallel lines.

Another exercise:
Two parallel lines and a transversal line intersecting them are shown.
Determine if the angles shown are alternate angles
b. Determine if they are alternate exterior angles.

Solution:
a. Yes, the angles in the figure are alternate angles. They are not on the same level and not on the same side of the transversal.
b. No. The angles are located in the internal part between the two parallel lines, therefore they are alternate angles but not exterior.

Additional exercise:
Here are two parallel lines and a line that intersects them.
Find the size of angle $W$
and determine whether angle W and angle $Q$ are alternate exterior angles.
Given that: $Q=120$

Solution:
According to the given information, we can determine that angle $W$ and angle $Q$ are alternate angles. They are located between two parallel lines, each on a different side of the transversal and not on the same level.
Alternate angles are equal to each other, therefore if $Q=120$ we can conclude that angle $W=120$

Additionally, we can determine that the two angles are alternate exterior angles due to the fact that they are both located on the outer side of the lines.

Additional Exercise:
Determine in which of the drawings there are equal alternate exterior angles and explain why.
In all drawings, the two lines are parallel to each other.

1.

2.

Solution:
In the first drawing, the two angles are alternate exterior angles since they are located in the external part of the lines
and in the second drawing, the two angles are alternate interior angles since they are located in the internal part of the lines.

More exercises:
Determine true or false:

Between parallel lines-
a. Alternate exterior angles are not equal to each other.
b. Alternate exterior angles are located in the external part outside both parallel lines.
c. Alternate angles sum to $180$.

Solution:
a. Incorrect – alternate exterior angles are equal to each other (and alternate interior angles are equal to each other).
b. Correct – this is why they are called alternate exterior angles.
c. Incorrect – alternate angles are not supplementary to $180$ but are equal to each other (regardless of whether they are exterior or interior).