SM2 13.1-5: Inscribed Angles, v1

Added: 2026-05-06

[00:00:00]Hello and welcome. So given a circle, the  information below, find the specified information.

[00:00:05]So first off, we're given the measure of ADC. So A to D to C is 87 degrees. We're told the measure of angle ACB, so ACB, is going to  be 49 degrees. And the measure of arc C to D is 64 degrees. So we're given that arc, we're given  this angle, and we're given this angle, okay?

[00:00:32]So now essentially we need to find the resulting  information. Well, a couple of things. First off, remember central angles and inscribed angles. A  central angle is an angle formed at the center of the circle and it matches, it equals, whatever  the measure of the arc it is resulting from, okay?

[00:00:51]So looking at this one, if the central angle is  40 degrees, the measure of the arc, also 40.

[00:00:57]Inscribed angles is what we're mainly going to be  using for this problem. It's the angles formed on the outside, the circumference of the circle, and  the angle will be half of whatever it is the arc is. So if the arc is 80 degrees, then the angle is 40  degrees. You could also say this is a doubling relationship where the arc is double whatever  the angle is. So again, if the arc is-- the angle is like 20, the arc would be 40, okay? So that is your central  and inscribed angles. So we'll look at the yellow angle, 49. If we extend it out, here's its arc,  right? You just follow those lines out. And how we can find that, we say, all right, well, the  angle is half of the arc. So if we take 49 and we double it, we get 98. There's your arc. 87,  that is our angle, right? We extend it out, here's the arc, right? And then from there all we  have to do is 87, double it, 174. There's the arc, okay? And now we're practically done. If we wanted  to find more information, let's say we wanted to find the inscribed angle forming 64. All we have  to do is do 64, half it, there's 32, right? If we wanted to find our last little remaining arc  over here, well, notice something really quick.

[00:02:15]The entire circle is 360 degrees, right? Well,  what we're looking for, that little blue segment, is essentially the whole circle except for that.  So if we take 360, the whole way around a circle, and we take the 64, the 174, and the 98 out,  that will leave our remaining blue portion of the arc. All right, so 360 minus the other three  arcs, 64, 174, and 98, we end up with 24 degrees.

[00:02:45]And that is our little arc right there. Now if we  were to follow that 24 degrees in, right, up there, you'll notice it's this little inscribed angle.  And with half of the arc, so half of 24 is 12.

[00:03:02]And that is everything you're  going to be able to find for this, okay? So if we want to just state the information  down below: the measure of arc AC, 174 degrees.

[00:03:13]The measure of arc AB we found to be 98 degrees,  that's our yellow arc. The measure of arc DB we just found, that was our blue arc, 24 degrees. And  then our last but not least, our angle BCD, which we just found to be 12 degrees. And that's it.  That's as crazy as it gets. Thanks for watching.