### Video Transcript

Given that the measure of angle
ππ΄πΆ equals 48 degrees, find πΏ.

Letβs identify what we know based
on this image. The figure tells us that line
segment π΄πΆ is parallel to line segment ππ΅. Since these two lines are parallel,
this angle ππ΄πΆ and this angle π΄ππ΅ are supplementary angles. The two of them when added together
equal 180 degrees.

We know that ππ΄πΆ is 48
degrees. If we solve this statement, we can
find the measure of angle π΄ππ΅. Subtract 48 degrees from both
sides, and we find out that the measure of angle π΄ππ΅ is 132 degrees. This is not enough information to
solve. We also need to know this: the
measure of an inscribed angle.

For us, the angle π΅πΆπ΄ is half
the measure of the central angle subtended by the same arc. Which angle is that? That would be this angle. The measure of angle π΅πΆπ΄ is
equal to one-half of the central angle. But how will we find out what the
central angle is?

We know that a circle is 360
degrees, and we know that the measure of angle π΄ππ΅ is 132 degrees. 360 minus 132 equals 228
degrees. The central angle subtended by the
arc π΅πΆπ΄ equals 228 degrees. One-half of 228 equals 114 degrees,
and that means πΏ equals 114 degrees.