On the diagram, there is a quadrilateral within a circle. As you can see, each corner of the quadrilateral touches the circumference of the circle, this indicates that this quadrilateral is a cyclic quadrilateral.
A characteristic of a cyclic quadrilateral is that the opposite angles are supplementary.
Knowing this, you can determine the values of x and y as follows:
[tex]\begin{gathered} x+100º=180º\text{ \rightarrow{}subtract 100º to both sides of the equal sign} \\ x+100º-100º=180º-100º \\ x=80º \end{gathered}[/tex][tex]\begin{gathered} 2y+102º=180º\text{ \rightarrow subtract 102º to both sides of the expression} \\ 2y+102º-102º=180º-102º \\ 2y=78º\text{ \rightarrow Divide both sides by 2} \\ \frac{2y}{2}=\frac{78º}{2} \\ y=39º \end{gathered}[/tex]
The value of x is 80º and the value of y is 39º
