### Video Transcript

In the figure, what is the measure of angle ๐ท๐น๐?

Angle ๐ท๐น๐ is located here. There are multiple ways to solve for the measure of angle ๐ท๐น๐. But they all rely on one thing โ the fact that these two lines run parallel. So these here are our parallel lines and a line going through this pair of parallel lines is called the transversal. And thereโre properties that we know when using parallel lines and a transversal that will help us solve for the measure of angle ๐ท๐น๐.

So weโre given the angle ๐ต๐๐ธ, the measure of that is 101 degrees. These two blue angles will be considered alternate exterior angles. Theyโre on alternate sides of the transversal: one is on the left-hand side and one is on the right. And theyโre both on the exterior of the parallel lines. So theyโre both outside of the pink lines. And the great thing about alternate exterior angles is theyโre congruent. So the measure of angle ๐๐น๐ถ would also be 101 degrees.

Now, these two angles create a line. So we can call them a linear pair or theyโre supplementary angles. They add to 180 degrees and the reason why is a straight line is 180 degrees. And measure, so we can call the measure of angle ๐ท๐น๐ โ the one that weโre looking for โ ๐ฅ. The measure of angle ๐๐น๐ถ is equal to 101 degrees and we set it equal to 180 degrees. So to solve for ๐ฅ, we need to subtract 101 degrees from both sides of the equation. And we find that ๐ฅ is equal to 79 degrees. Therefore, the measure of angle ๐ท๐น๐ is equal to 79 degrees.

Letโs also show one more way that we could have solved this problem. Instead of using the alternate exterior angles, these two angles in green would be considered corresponding angles. They need to be on the same side of the transversal and theyโre both on the left. One needs to be on the inside of the parallel lines and one needs to be on the outside of the parallel lines. And we have that. And the great thing about corresponding angles is theyโre also congruent. So the measure of angle of ๐ท๐น๐ would be 101 degrees.

So now, we can still use the fact that the green and the yellow are considered a linear pair because they also make a straight line. So like we said, the measure of angle ๐ท๐น๐ is 101 degrees. And we can let the measure of angle ๐ท๐น๐ what weโre solving for be ๐ฅ and set it equal to 180 degrees. So just as before, we solve for ๐ฅ by subtracting 101 from both sides of the equation. And once again, we get 79 degrees.

So in this figure, the measure of angle ๐ท๐น๐ is 79 degrees.