Angle subtended by a chord/arc of a circle
- [Voiceover] A circle is centered on point B. We see that right over there. That's the center of this big, blue circle. Points A, C, and D lie on its circumference. We see that. Points A, C, and D lie on the circumference. If angle ABC... So ABC; So that's this central angle right over here; measures 132 degrees. Alright, so this is 132 degrees. What does angle ADC measure? A, D, C. So let's think about how these are related. ABC is a central angle. ADC is an inscribed angle. And they intercept the same arc. The arc AC. They both intercept this arc right over here. And we know from the inscribed angle theorem that an inscribed angle that intercepts the same arc as a central angle is going to have half the angle measure. And it even looks that way right over here. So if ABC- if the central angle is 132 degrees, then the inscribed angle that intercepts the same arc is going to be half of that. So half of 132 degrees is what? It is 66 degrees. We can check our answer, and we got it right.