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Inscribed shapes: find inscribed angle

Using either the inscribed angle theorem or the fact that two inscribed angles that intercept the same arc must be congruent.

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Video transcript

- So what I would like you to do is see if you can figure out the measure of angle DEG here. So try to figure out the measure of this angle. I encourage you to pause the video now and try it on your own. All right, now let's work through this together and the key realization here is to think about this angle, it is an inscribed angle, we see it's vertexes sitting on the circle itself. And then think about the arc that it intercepts. And we see, we see that it intercepts, so let me draw these two sides of the angle, we see that it intercepts arc CD. It intercepts arc CD. And so the measure of this angle, since it's an inscribed angle, is going to be half the measure of arc CD. So if we could figure out the measure of arc CD, then we're going to be in good shape. Because if we figure out the measure of arc CD, then we take half of that and we'll figure out what we care about. Well, what you might notice, is that there's another inscribed angle that also intercepts arc CD. We have this angle right over here. It also intercepts arc CD. So you could call this angle C ... Whoops. You could call this angle CFD. This also intercepts the same arc. So there's two ways you could think about it. Two inscribed angles that intercept the same arc are going to have the same angle measure so just off of that you could say that this is going to be, that these two angles have the same measure, so you could say this is going to be 50 degrees. Or you could go, you could actually solve what the measure of arc CD is. It's going to be twice the measure of the inscribed angle that intercepts it. So the measure of arc CD is going to be 100 degrees. Twice the 50 degrees. And then you use that and you say, Well, if the measure of that arc is 100 degrees, then an inscribed angle that intercepts it is going to have half its measure, it's going to be 50 degrees. So either way we get to 50 degrees.