### Video Transcript

Given that the measure of angle
ππ΄πΆ equals 36 degrees, determine the measure of angle π΅π΄π and the measure of
angle π΄ππΆ.

We want to know the measure of
angle π΅π΄π and the measure of angle π΄ππΆ. Letβs start by identifying what we
know. We know that the measure of angle
ππ΄πΆ is 36 degrees, so we can add that to the diagram. Weβll also wanna list other
information we can identify from the diagram. We know that line segment π΄πΆ and
the line segment π΄π΅ are tangent to the circle π since each segment intersects the
circle at exactly one point. Line segment π΄πΆ and line segment
π΄π΅ intersect at point π΄. From there, we say that line
segment ππΆ and the line segment ππ΅ are radii of circle π. We can take these four pieces of
information and draw some conclusions.

We can say that line segment π΄πΆ
is equal to line segment π΄π΅ in length, since this is one of the properties of
tangents when they intersect at an external point. We can also say, based on circle
properties, that the line segment ππ΄ bisects the angle π΅π΄πΆ. This is another one of our circle
theorems. And since thatβs true, angle π΅π΄π
has to be equal in measure to angle ππ΄πΆ. And angle ππ΄πΆ is 36 degrees,
which makes angle π΅π΄π 36 degrees. Thatβs the first part of the
question.

Now weβre moving on to find the
angle of π΄ππΆ. We recognize that the points π΄,
πΆ, and π form a triangle. And since the line segment π΄πΆ is
tangent to this circle at point πΆ, thereβs a right angle here. The measure of angle ππΆπ΄ is 90
degrees. And once we see that, we can say
that 90 degrees plus 36 degrees plus our missing angle must equal 180 degrees
because we know the sum of interior angles in triangles must be 180. 90 plus 36 is 126. And when we subtract 126 degrees
from both sides, we see that the measure of angle π΄ππΆ is 54 degrees.