# Question Video: Finding the Measure of an Angle given Its Arcβs Measure Using Another Inscribed Angle Mathematics

Given that πβ π΅π΄π· = 36Β° and πβ πΆπ΅π΄ = 37Β°, find πβ π΅πΆπ· and πβ πΆπ·π΄.

01:37

### Video Transcript

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

Letβs 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 πΆπ΅π΄ is equal to 37. We are looking to calculate the measure of angle π΅πΆπ·, which is this one, and the measure of angle πΆπ·π΄, which is this one. We now observe that the first unknown angle, thatβs π΅πΆπ·, 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΅πΆπ·. But of course, weβve now seen that thatβs 36 degrees.

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