### 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.

Weβll begin by adding the
information in the question to the diagram. The measure of angle ππ΄πΆ is
36 degrees. We need to find the measures of
angles π΅π΄π and π΄ππΆ. First, we should know that π΄
is a point exterior to the circle. The line segments π΄πΆ and π΄π΅
are tangents of the circle, and the line segment π΄π is the line segment
connecting this exterior point to the center of the circle. We can recall that the line
connecting an exterior point to the center of a circle bisects the angle formed
by two tangents from that point to the circle. So at point π΄, the measures of
angles ππ΄π΅ and ππ΄πΆ are equal. We know the measure of angle
ππ΄πΆ is 36 degrees, and so the measure of angle ππ΄π΅ or angle π΅π΄π is also
36 degrees.

Weβll now find the measure of
angle π΄ππΆ, and to do this, weβll consider triangle π΄ππΆ. π΄πΆ is a tangent of the circle
and ππΆ is a radius. We recall that any tangent to a
circle is perpendicular to the radius at the point of contact, and so the angle
ππΆπ΄ is a right angle. Using the fact that the angle
sum in any triangle is 180 degrees, we find the measure of angle π΄ππΆ by
subtracting the measures of the other two angles in triangle π΄ππΆ from 180
degrees, which gives 54 degrees. The measure of angle π΅π΄π is
36 degrees, and the measure of angle π΄ππΆ is 54 degrees.