Video Transcript
In the figure, line segment 𝐵𝐷 is a diameter. What is the measure of angle 𝐴𝐶𝐷?
And then we’ve got a diagram of a circle with four points 𝐴, 𝐵, 𝐶, 𝐷 lying on the circumference. We’re told that line segment 𝐵𝐷 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, that’s angle 𝐵𝐶𝐷; it’s 90 degrees. So, how does this help us?
Well, we’re trying to find angle 𝐴𝐶𝐷, which we can mark on our diagram as 𝜃. Since we know that both 𝐴𝐶𝐷 and 𝐵𝐶𝐴 sum to 90 degrees, we can form and solve an equation for 𝜃. That is, 64.5 degrees plus 𝜃 equals 90 degrees. Then, we solve for 𝜃 by subtracting 64.5 from both sides. 90 minus 64.5 is 25.5. So, the measure of angle 𝐴𝐶𝐷 is 25.5 degrees.
