### Video Transcript

Which of the following is the
correct relation between the angles of triangle 𝐴𝐵𝐶? Option (A) the measure of angle 𝐴
is greater than the measure of angle 𝐵 is greater than the measure of angle 𝐶. Option (B) the measure of angle 𝐵
is greater than the measure of angle 𝐴 is greater than the measure of angle 𝐶. Option (C) the measure of angle 𝐶
is greater than the measure of angle 𝐵 is greater than the measure of angle 𝐴. Option (D) the measure of angle 𝐴
is greater than the measure of angle 𝐶 is greater than the measure of angle 𝐵. Or is it option (E) the measure of
angle 𝐶 is greater than the measure of angle 𝐴 is greater than the measure of
angle 𝐵?

In this question, we are given the
side lengths of a triangle, 𝐴𝐵𝐶. And we are asked to use this to
determine the correct relationship between the measure of its interior angles. Since we want to compare the
measures of the interior angles of the triangle by using the side lengths, we can
recall the angle comparison theorem in triangles. This tells us that in any triangle,
the angle opposite the longer side will have measure larger than an angle that is
opposite a shorter side. This means that we can compare the
measures of the interior angles of a triangle by comparing the lengths of the sides
opposite the angle.

In this triangle, we can see that
side 𝐵𝐶 is the longest, with length 29.7. We then see that side 𝐴𝐵 is the
next longest, with length 21.3. Finally, side 𝐴𝐶 is the shortest,
with length 21.

We can then use this, combined with
the angle comparison theorem in triangles, to compare the measures of the interior
angles. Remember, the angle opposite the
longer side will have larger measure. We see that angle 𝐴 is opposite
the longest side, so it has the largest measure. And we see that angle 𝐶 is
opposite the second-longest side, so it has the second-largest measure. Finally, we can see that angle 𝐵
is opposite the shortest side, so it has the smallest measure. This gives us that the measure of
angle 𝐴 is greater than the measure of angle 𝐶 is greater than the measure of
angle 𝐵, which we can see is option (D).