Question Video: Identifying an Angle given Its Supplementary Angles Mathematics

Given that 𝐹 lies on the straight line between 𝐴 and 𝐡, determine which angle supplements ∠𝐴𝐹𝐢.

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Video Transcript

Given that 𝐹 lies on the straight line between 𝐴 and 𝐡, determine which angle supplements angle 𝐴𝐹𝐢.

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 𝐴𝐹𝐢. To do this, we can start by marking angle 𝐴𝐹𝐢 on the diagram. It is the smaller rotation required to rotate the ray from 𝐹 through 𝐴 onto the ray from 𝐹 through 𝐢 using 𝐹 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 𝐡𝐹𝐴 is 180 degrees. We want to find an angle whose measure we can add to the measure of angle 𝐴𝐹𝐢 to be 180 degrees. If we mark the following angle on the diagram, we see that it is adjacent to angle 𝐴𝐹𝐢, 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 angles’ measures is 180 degrees, they must be supplementary. We can see that angles 𝐴𝐹𝐢 and 𝐡𝐹𝐢 are supplementary.

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