### Video Transcript

Given that the measure of angle π΄ππ· equals 41.5 degrees, find the measure of angle π΅ in degrees.

And then we have a diagram showing a circle, center π, with four points on its circumference π΄, π΅, πΆ, and π·. Weβre given that the measure of angle π΄ππ· is 41.5 degrees. So, letβs add that to our diagram. Angle π΄ππ· lies at the center of the circle as shown. This angle is said to subtend the arc π·π΄. Now, in fact, thereβs an arc thatβs equal in length to arc π·π΄. Itβs arc πΆπ· as represented by these dashed lines. And since the arc lengths are equal, we can say that the measure of arc π·π΄ must be equal to the measure of arc πΆπ·. But of course, the measure of an arc is simply the angle that that arc makes at the center of the circle. So, the measure of arc π·π΄ is 41.5 degrees, meaning that the measure of arc πΆπ· must also be 41.5 degrees.

We can now add that angle to our diagram too. And in fact, this is really useful because we can now calculate the measure of angle πΆππ΄. Itβs 41.5 plus 41.5, which is 83 degrees. Now, weβre trying to find the measure of angle π΅ in degrees, and we now have everything we need to do so. We can use the inscribed angle theorem that links the angle at the center of the circle with the inscribed angle at its circumference. This theorem tells us that an inscribed angle is going to be equal to half of the central angle that subtends the same arc on that circle. The inscribed angle at π΅ subtends arc πΆπ΄, as does the angle at the center of the circle πΆππ΄. So, the measure of angle π΅ must be a half of the measure of angle πΆππ΄. In other words, itβs a half of 83 degrees, which is 41.5 degrees.

The measure of angle π΅ then is 41.5 degrees.