Alternate Exterior Angles

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.