### Video Transcript

π is a circle, where line segment
π΄π΅ is a chord and line πΆπ· is a tangent. If π΄π΅ is parallel to πΆπ· and the
measure of arc π΄π΅ is 72 degrees, find the measure of arc π΅πΆ.

Since π΄π΅ is parallel to πΆπ·,
where π΄π΅ is a chord and πΆπ· is a tangent, thereβs a theorem we can use. Weβre going to use the theorem that
says that the measure of the arcs between a parallel chord and tangent of a circle
are equal. So we can say that the measure of
arc π΄πΆ must be equal to the measure of arc π΅πΆ. In fact, the question tells us that
the measure of arc π΄π΅ is 72 degrees. And we can use the fact that the
sum of all the measures of all arcs which make up the circle is 360 degrees. This means that the measure of arc
π΄πΆ plus the measure of arc π΄π΅, which is 72 degrees, plus the measure of arc π΅πΆ
is 360. Then, we subtract 72 degrees from
both sides. And we find that the measure of arc
π΄πΆ plus the measure of arc π΅πΆ is 288 degrees.

But earlier, we stated that the
measure of arc π΄πΆ is equal to the measure of arc π΅πΆ. So we can say that two times the
measure of arc π΅πΆ is 288 degrees. And then we could divide both sides
of this equation by two. So the measure of arc π΅πΆ is 288
divided by two, which is in fact 144 degrees. The measure of arc π΅πΆ is 144
degrees.