Video Transcript
In the following triangle 𝐴𝐵𝐶,
if the measure of angle 𝐶 equals the measure of angle 𝐶𝐴𝐷 equals 43 degrees and
the measure of angle 𝐵 equals the measure of angle 𝐵𝐴𝐷, find the measure of
angle 𝐵𝐴𝐶.
We can start this question by
identifying the two pairs of congruent angle measures. We have that the measure of angle
𝐶 is equal to the measure of angle 𝐶𝐴𝐷, and those are both 43 degrees. We also have that the measure of
angle 𝐵 is equal to the measure of angle 𝐵𝐴𝐷, although we aren’t given an exact
measurement for those. We can then identify that the angle
that we wish to calculate is that of the measure of angle 𝐵𝐴𝐶, which occurs at
the vertex 𝐴 in the larger triangle 𝐴𝐵𝐶.
A property that we can apply in
this question is that the sum of the measures of the interior angles in a triangle
is 180 degrees. So then, if we consider the large
triangle 𝐴𝐵𝐶, we can say that the measure of angle 𝐵𝐴𝐶 plus the measure of
angle 𝐵 plus the measure of angle 𝐶 is equal to 180 degrees. From the diagram then, we can
observe that the measure of angle 𝐵𝐴𝐶 actually consists of an angle of 43 degrees
and the measure of angle 𝐵𝐴𝐷.
Then, we are given in the question
that the measure of angle 𝐵 is equal to the measure of angle 𝐵𝐴𝐷. Adding in the measure of angle 𝐶,
which is 43 degrees, we can add the left-hand side, and it will be equal to 180
degrees. We can then simplify this by adding
the two 43 degrees, which is 86 degrees. And we know that there will be two
lots of the measure of angle 𝐵𝐴𝐷. Subtracting 86 degrees from both
sides, we have that two times the measure of angle 𝐵𝐴𝐷 is equal to 94
degrees. Finally, dividing through by two,
we have that the measure of angle 𝐵𝐴𝐷 is 47 degrees. Now that we know the measure of
this angle, we can calculate the measure of angle 𝐵𝐴𝐶. It will be equal to 43 degrees plus
47 degrees, which gives us a final answer of 90 degrees.
