Video Transcript
Which is the correct relationship? Option (A) the measure of angle 𝐵 is greater than the measure of angle 𝐶. Option (B) the measure of angle 𝐵 is equal to the measure of angle 𝐶. Or is it option (C) the measure of angle 𝐵 is less than the measure of angle 𝐶?
In this question, we are given two side lengths of a triangle and asked to use this
to compare the measures of two of the interior angles of the triangle. To do this, we can start by adding the two angles whose measure we want to compare on
the diagram.
We can then note that we are given the lengths of the sides opposite these two
angles. We can then recall that in a triangle, the angle opposite the longer side will have
larger measure. This is called the angle comparison theorem in triangles. Therefore, since the angle at 𝐶 is opposite a side longer than that opposite angle
𝐵, we can say that the measure of angle 𝐶 is greater than the measure of angle
𝐵.
We can then switch the direction of this inequality to obtain that the measure of
angle 𝐵 is less than the measure of angle 𝐶, which we can see matches option
(C).
