### Video Transcript

Given that πΉ lies on the straight line between π΄ and π΅, determine which angle supplements angle π΄πΉπΆ.

In this question, we are given a figure containing multiple labeled points and rays between the points and asked to determine which angle supplements angle π΄πΉπΆ. To do this, we can start by marking angle π΄πΉπΆ on the diagram. It is the smaller rotation required to rotate the ray from πΉ through π΄ onto the ray from πΉ through πΆ using πΉ as the center of rotation.

We can then recall that we call two angles supplementary if their measures sum to 180 degrees. We know that a straight angle has a measure of 180 degrees. So we can mark on the figure that the measure of angle π΅πΉπ΄ is 180 degrees. We want to find an angle whose measure we can add to the measure of angle π΄πΉπΆ to be 180 degrees. If we mark the following angle on the diagram, we see that it is adjacent to angle π΄πΉπΆ, and the two angles combine to make a straight angle. This means that the sum of their measures must be 180 degrees.

Since the sum of these anglesβ measures is 180 degrees, they must be supplementary. We can see that angles π΄πΉπΆ and π΅πΉπΆ are supplementary.