Question

Find the value of x and y for each diagram.

Short answer

The values of x and y are 33 and 66 respectively.

Step-by-step solution

Step 1. Label the given diagram.

Label the figure as shown:

Step 2. Write the relation between the angles BOF and AOE.

From the given diagram it can be noticed that the angles BOF and AOE are the vertically opposite angles.

Therefore,$\angle BOF=\angle AOE$

Step 3. Find the value of x.

Find the value of x by using the fact that $\angle BOF=\angle AOE$.

Therefore,

$$\begin{gathered} \angle BOF=\angle AOE \\ 2x-16=50 \\ 2x=50+16 \\ 2x=66 \\ x=\frac{66}{2} \\ x=33 \end{gathered}$$

Therefore, the value of x is 33.

Step 4. Find the measure of the angle COF.

As the value of x is 33 and the measure of the angle COF is x.

Therefore, the measure of the angle COF is:

$x=33$

Therefore, the measure of the angle COF is 33°.

Step 5. Write the relation between the angles COF and EOD.

From the diagram, it can be noticed that the angles COF and EOD are vertically opposite angles.

Therefore, $\angle COF=\angle EOD$.

Step 6. Find the value of y.

As, $\angle COF=\angle EOD$.

Therefore,

$$\begin{gathered} \angle COF=\angle EOD \\ 33=3\left(33\right)-y \\ 33=99-y \\ y=99-33 \\ y=66 \end{gathered}$$

Therefore, the value of y is 66.