Find the value of x and y for each diagram.

Label the figure as shown:

From the given diagram it can be noticed that the angles AOD and AOC lies on the straight line CD.

Therefore, the sum of the angles AOD and AOC is 180°.

Therefore,$\angle AOD+\angle AOC=180°$

Find the value of x by using the fact that $\angle AOD+\angle AOC=180°$.

Therefore,

$$\begin{gathered} \angle AOD+\angle AOC=180° \\ x+3x-8=180 \\ 4x=180+8 \\ 4x=188 \\ x=\frac{188}{4} \\ x=47 \end{gathered}$$

Therefore, the value of x is 47.

As, the value of x is 47 and the measure of the angle AOC is $3x-8$.

Therefore, the measure of the angle AOC is:

$3x-8=3\left(47\right)-8=141-8=133$

Therefore, the measure of the angleAOC is 133°.

From the diagram it can be noticed that the angles AOC and BOD are vertically opposite angles.

Therefore, $\angle AOC=\angle BOD$.

As, $\angle AOC=\angle BOD$.

Therefore,

$$\begin{gathered} \angle AOC=\angle BOD \\ 133=2y-17 \\ 133+17=2y \\ 150=2y \\ \frac{150}{2}=y \\ 75=y \end{gathered}$$

Therefore, the value of y is 75.