### Video Transcript

Find the measures of the angles of
triangle π΄π΅πΆ.

Letβs begin by considering the
figure that we are given. We can see that there are two
parallel lines marked on the diagram, the ray π΄π· and the line segment π΅πΆ. And we also have two congruent line
segments, which are π΄πΆ and π΅πΆ. Letβs consider the angle π·π΄πΆ,
which is created by transversal π΄πΆ between the two parallel lines. The angle π΄πΆπ΅ is alternate to
the angle π·π΄πΆ, and so these will both have a measure of 39.5 degrees.

Next, we can return to the two
congruent line segments. These are part of the triangle
π΄π΅πΆ, and so, by definition, this is an isosceles triangle. Thatβs because we can recall that
an isosceles triangle has two congruent sides. And by the isosceles triangle
theorem, we know that the angles opposite the congruent sides in an isosceles
triangle are congruent.

In triangle π΄π΅πΆ, these congruent
base angles will be angle π΅π΄πΆ and angle π΄π΅πΆ. As these will both have the same
measure, we can define them with the same letter, for example, the letter π¦. Since we know that the internal
angle measures in a triangle sum to 180 degrees, we can write that the three angles
of π¦, π¦, and 39.5 degrees sum to give 180 degrees. And simplifying the π¦ plus π¦
gives us two π¦. We can then subtract 39.5 degrees
from both sides to give us that two π¦ equals 140.5 degrees. Finally, dividing both sides by
two, we have that π¦ equals 70.25 degrees.

We have therefore found all three
of the required angle measures in triangle π΄π΅πΆ. The measure of angle π΄π΅πΆ is
70.25 degrees. The measure of angle π΅π΄πΆ is also
70.25 degrees. And the first angle that we
determined, the measure of angle π΄πΆπ΅, is 39.5 degrees.