### Video Transcript

Consider the given circle. Find the measure of the arc πΆπ·.

We recall first that the arc πΆπ· means the minor arc between points πΆ and π·. Thatβs this arc here on the diagram. We recall also that the measure of an arc is the measure of its central angle. Thatβs the angle between the two radii connecting the endpoints of the arc to the center of the circle. For the arc πΆπ·, the two radii are the line segments πΆπ and π·π. So the central angle for this arc is angle πΆππ·. If we want to determine the measure of the arc πΆπ· then, we need to determine the measure of the angle πΆππ·.

Now, in the figure, weβre given the measures of two other angles: angle π΅ππΆ, which is 56 degrees, and angle π΄ππ·, which is 32 degrees. Now, as the line segment π΄π΅ is a diameter of the circle, so it is a straight line, the measures of the three angles π΅ππΆ, πΆππ·, and π΄ππ· must sum to 180 degrees. We can therefore form an equation. 56 degrees plus the measure of angle πΆππ· plus 32 degrees equals 180 degrees. We can find the measure of angle πΆππ· by subtracting 56 degrees and 32 degrees from each side of the equation. The measure of angle πΆππ· is 180 degrees minus 56 degrees minus 32 degrees, which is 92 degrees. Angle πΆππ· is the central angle for the arc πΆπ·. So the measure of the arc πΆπ· is also 92 degrees.