### Video Transcript

Find the measure of angle πΆ.

We can see from the diagram that
the line π΄π΅ is parallel to the line πΆπ·. In this question, we need to
calculate the measure of angle πΆ. We begin by looking at the point
π΄, noting that angles at a point or in a circle sum to 360 degrees. If we let the missing angle be π₯,
then π₯ plus 123 plus 132 is equal to 360. Simplifying this gives us π₯ plus
255 is equal to 360. Subtracting 255 from both sides of
this equation gives us π₯ is equal to 105. The missing angle at point π΄ is
105 degrees.

As mentioned previously, lines π΄π΅
and πΆπ· are parallel. The line π΄πΆ creates two
cointerior or supplementary angles. As these sum to 180 degrees, the
angle π¦ at point πΆ plus 105 must equal 180. Subtracting 105 from both sides of
this equation gives us π¦ is equal to 75. We can therefore conclude that the
measure of angle πΆ is equal to 75 degrees.