### Video Transcript

Which of the following angle pairs are alternate interior angles? Angle ๐ and angle ๐; angle ๐ and angle ๐; angle ๐ and angle โ; angle ๐ and angle ๐; or angle ๐ and angle ๐.

Looking at the diagram, we can see that the setup in this question is one where when we have two lines and then a transversal โ that is a line that crosses both of the other lines. And we have 12 angles formed, where these lines intersect. Weโre asked to determine which of the angle pairs are alternate interior angles.

The definition of alternate interior angles is nonadjacent interior angles on opposite sides of the transversal. Now, most of the angle pairs that weโve been asked about are in the bottom part of the diagram. So weโll consider the horizontal line shaded in green as the transversal. The part of the diagram now shaded in orange is the interior of the two black lines. So letโs consider the positioning of each of these angle pairs in turn.

Firstly, angles ๐ and ๐: well, we can see that they are indeed on opposite sides of the transversal. But theyโre on the exterior of the black lines. Therefore, ๐ and ๐ are in fact an example of alternate exterior angles and so not the right type of angles that weโre looking for.

Next, letโs consider the angles pair ๐ and ๐. We can see that they are on the interior of the diagram. But theyโre on the same side of the transversal. Therefore, angles ๐ and ๐ are whatโs known as consecutive interior angles. So again, theyโre not the right type of angles.

The same is true of angles ๐ and โ. They are on the interior of the diagram, but on the same side of the transversal. Theyโre also consecutive interior angles. Next, letโs consider the angle pair ๐ and ๐. Now, looking at these, we can see that they are on the interior of the diagram and this time they are on opposite sides of the transversal. Theyโre also not adjacent. And therefore, they are an example of alternate interior angles. So we have found one pair of angles that are alternate interior the angles.

Now, to consider angles ๐ and ๐, we actually need to change the setup slightly in terms of which line weโre considering to be the transversal. The transversal in relation to this pair of angles is the line that Iโve now marked in green. The interior of the diagram is now the part inside the two black lines.

Looking at angles ๐ and ๐, we can see that ๐ is an interior angle, but ๐ is an exterior angle. They both lie on the same side of the transversal and they both lie on the same side of their black line. Therefore, angles ๐ and ๐ are whatโs known as corresponding angles.

So of the five options given, the only pair of angles that are alternate interior angles are angle ๐ and angle ๐.