91Ó°ÊÓ

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,$∠AOD+∠AOC=180°$

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

Therefore,

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

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, $∠AOC=∠BOD$.

As, $∠AOC=∠BOD$.

Therefore,

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

Therefore, the value of y is 75.