### Video Transcript

In the following triangle π΄π΅πΆ,
if the measure of angle πΆ equals the measure of angle πΆπ΄π· equals 43 degrees and
the measure of angle π΅ equals the measure of angle π΅π΄π·, find the measure of
angle π΅π΄πΆ.

We can start this question by
identifying the two pairs of congruent angle measures. We have that the measure of angle
πΆ is equal to the measure of angle πΆπ΄π·, and those are both 43 degrees. We also have that the measure of
angle π΅ is equal to the measure of angle π΅π΄π·, although we arenβt 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 π΅π΄πΆ, which occurs at
the vertex π΄ in the larger triangle π΄π΅πΆ.

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 π΄π΅πΆ, we can say that the measure of angle π΅π΄πΆ plus the measure of
angle π΅ plus the measure of angle πΆ is equal to 180 degrees. From the diagram then, we can
observe that the measure of angle π΅π΄πΆ actually consists of an angle of 43 degrees
and the measure of angle π΅π΄π·.

Then, we are given in the question
that the measure of angle π΅ is equal to the measure of angle π΅π΄π·. Adding in the measure of angle πΆ,
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 π΅π΄π·. Subtracting 86 degrees from both
sides, we have that two times the measure of angle π΅π΄π· is equal to 94
degrees. Finally, dividing through by two,
we have that the measure of angle π΅π΄π· is 47 degrees. Now that we know the measure of
this angle, we can calculate the measure of angle π΅π΄πΆ. It will be equal to 43 degrees plus
47 degrees, which gives us a final answer of 90 degrees.