Video Transcript
In the figure, line segment π΅π· is a diameter. What is the measure of angle π΄πΆπ·?
And then weβve got a diagram of a circle with four points π΄, π΅, πΆ, π· lying on the circumference. Weβre told that line segment π΅π· is a diameter. It passes through the center of the circle. So we can use the following theorem. This theorem tells us that the angle subtended by a diameter is 90 degrees. In this case, thatβs angle π΅πΆπ·; itβs 90 degrees. So, how does this help us?
Well, weβre trying to find angle π΄πΆπ·, which we can mark on our diagram as π. Since we know that both π΄πΆπ· and π΅πΆπ΄ sum to 90 degrees, we can form and solve an equation for π. That is, 64.5 degrees plus π equals 90 degrees. Then, we solve for π by subtracting 64.5 from both sides. 90 minus 64.5 is 25.5. So, the measure of angle π΄πΆπ· is 25.5 degrees.