### Video Transcript

Given that the measure of angle
π΅π΄π· is equal to 36 degrees and the measure of angle πΆπ΅π΄ is equal to 37
degrees, find the measure of angle π΅πΆπ· and the measure of angle πΆπ·π΄.

Letβs begin by adding the angles
that we know onto the diagram. The measure of angle π΅π΄π· is
equal to 36 degrees, and the measure of angle πΆπ΅π΄ is equal to 37. We are looking to calculate the
measure of angle π΅πΆπ·, which is this one, and the measure of angle πΆπ·π΄, which
is this one. We now observe that the first
unknown angle, thatβs π΅πΆπ·, is subtended by the same arc π΅π· as angle π΅π΄π·. And we know that inscribed angles
subtended by the same arc are equal. So the measure of angle π΅π΄π· must
be equal to the measure of angle π΅πΆπ·. But of course, weβve now seen that
thatβs 36 degrees.

In a similar way, we observed that
angle π΄π·πΆ is subtended from the same arc as angle π΄π΅πΆ. And so, these two angles are
congruent. The measure of angle π΄π΅πΆ must be
equal to the measure of angle π΄π·πΆ. And thatβs 37. So, using the property of inscribed
angles subtended from the same arc, we find the measure of angle π΅πΆπ· is equal to
36 degrees and the measure of angle πΆπ·π΄ is equal to 37 degrees.