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CCSS.Math:

a circle is centered on point B we see that right over there that's the center of this big blue circle points AC and D lie on its circumference we see that points a C and D line circumference if angle ABC so ABC so that's this central angle right over here measures 132 degrees all right 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 a DC 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 you could even 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