 This video is practice problem 3 in section 10.4, and we are asked to find x and y in the diagram. You'll notice that we have four inscribed angles in this diagram, and we call this an inscribed quadrilateral when we have a four-sided figure that is inscribed inside of a circle. We have a theorem regarding inscribed quadrilaterals that states is if a quadrilateral is inscribed in a circle, which this is, then opposite angles are supplementary. That means that angle B plus angle D will equal 180 degrees and angle A plus angle C will equal 180 degrees. We're going to solve this with two separate equations because angle B and D being supplementary both have x values will equal 180 degrees and then we'll do a separate equation with angle C or angle C and angle A that will add up to 180 degrees. So this is going to be just setting up the algebraic equations correctly and solving for the variable. Angle B plus angle D, I'm going to write down the terms, set them equal to 180 degrees and then solve. Combining like terms gives me 10x plus 10 equals 180 and then solving for x, I get x equals 17. Now we'll do a separate equation with angle A and angle C, setting them equal to 180 degrees and combining like terms, the two's cancel out. We get 9y equals 180 and y equals 20. You want to check your algebra on that, but when you come across these equations or these problems, just remember they're not equal to each other. Opposite angles in an inscribed quadrilateral are going to be supplementary.