 we're going to start section 10.4 inscribed angles with some vocabulary and we've already learned what a central angle is, but we're going to review that and find the similarities and the differences between an inscribed angle, a new term, and what we know about a central angle. So one thing about a central angle is that we know that the vertex is going to be at the center of a circle. So I'm just going to make a central angle here and call it ABC and I'm going to say that it's 80 degrees. So I would say that the measure of angle ABC equals 80 degrees. We will remember we want to put that M there and that make sure we know that it's a degree measure of an angle or an arc with the M. We know that on this central angle the intercepted arc is as you can extend these sides even and see that the intercepted arc is going to be arc AC and we learn that the measure of that intercepted arc is going to be equal to the central angle. So the central angle, 80 degrees, the intercepted arc AC is also 80 degrees. Now an inscribed angle is different because the vertex isn't the center, but the vertex will have be right on the circle and the sides will be cords of the circle. So if we create an inscribed angle ABC, it will look like this. The key thing being that vertex is going to be on the circle instead of the midpoint of the circle. So I can also label this angle ABC and let's just give that a measure of 30 degrees. I'm just putting that out there of 30 degrees. We still have an intercepted arc here AC because if we extend the cords here, that's where it's going to intercept the arc AC and we have a theorem that states that if an angle is inscribed in a circle, then the measure of the angle equals half the measure of its intercepted arc. So what that means to us is we know arc AC, the measure of that is going to be double the inscribed angle or you could think of it as the inscribed angle is half of the intercepted arc. So be aware of the relationships as we go forward in this section. If you're looking at central angles, the intercepted arcs will be equal and if you're looking at inscribed angles, we have that doubling relationship where the inscribed angle is going to be half of the intercepted arc.