Inscribed shapes: find inscribed angle

so what I would like you to do is see if you can figure out the measure of angle deg here so trying 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 its vertex it's sitting on is 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 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 in inscribed angle it's going to be half the measure of Arc CD so if we could figure out the measure of Arc CD then then we're going to be we're gonna be in good shape so 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 is 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 C F D 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 are going to 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 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