### Video Transcript

Find the measure of angle πΆπ΅π΄
and the measure of angle π·π΄πΆ.

The first angle measure that we
need to find is that of angle πΆπ΅π΄. This is part of the larger triangle
π΄π΅πΆ.

We observe that triangle π΄π΅πΆ has
two congruent line segments marked: π΄πΆ and π΅πΆ. That means that this is an
isosceles triangle, as an isosceles triangle is defined as a triangle that has two
congruent sides. We can then use the isosceles
triangle theorem, which states that in an isosceles triangle, the angles opposite
the congruent sides are congruent. In triangle π΄π΅πΆ, these two
congruent base angles will be angle πΆπ΄π΅ and angle πΆπ΅π΄. If we defined these angles to have
a measure of π₯ degrees, then we can write that π₯ degrees plus π₯ degrees plus 38
degrees equals 180 degrees.

Remember, we can set these three
angle measures equal to 180 degrees because the sum of the internal measures in a
triangle is 180 degrees. We can then simplify this by
collecting the like terms and then subtracting 38 degrees from both sides, which
gives us that two π₯ degrees is equal to 142 degrees. Dividing through by two, we have
that π₯ is equal to 71 degrees. So now we know the measure of both
the base angles in triangle π΄π΅πΆ. They are both 71 degrees. And thatβs the answer for the first
angle, since the measure of angle πΆπ΅π΄ is 71 degrees.

Now letβs consider the second angle
measure, which is the measure of angle π·π΄πΆ. Observe that we have this angle
π·π΄πΆ and the angle π·π΄π΅, which together form the larger angle πΆπ΄π΅ whose
measure we have already calculated as 71 degrees. If we knew the measure of angle
π·π΄π΅, we could calculate the measure of angle π·π΄πΆ.

Letβs take a closer look at
triangle π΄π΅π·. It has three congruent sides. And that means that triangle π΄π΅π·
is an equilateral triangle. And we know that an equilateral
triangle has all three angles congruent, which means they are all 60 degrees. So, the measure of angle π·π΄πΆ is
equal to 71 degrees minus 60 degrees, which is 11 degrees.

Therefore, we can give the answers
to both parts of the question. The measure of angle πΆπ΅π΄ is 71
degrees, and the measure of angle π·π΄πΆ is 11 degrees.