# Question Video: Identifying an Angle given Its Supplementary Angles Mathematics

Given that πΉ lies on the straight line between π΄ and π΅, determine which angle supplements β π΄πΉπΆ.

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### Video Transcript

Given that πΉ lies on the straight line between π΄ and π΅, determine which angle supplements angle π΄πΉπΆ.

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΄πΉπΆ. To do this, we can start by marking angle π΄πΉπΆ on the diagram. It is the smaller rotation required to rotate the ray from πΉ through π΄ onto the ray from πΉ through πΆ using πΉ 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΅πΉπ΄ is 180 degrees. We want to find an angle whose measure we can add to the measure of angle π΄πΉπΆ to be 180 degrees. If we mark the following angle on the diagram, we see that it is adjacent to angle π΄πΉπΆ, 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΄πΉπΆ and π΅πΉπΆ are supplementary.