Question

Find the value of x.

Short answer

The value of x is 25.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Label the given figure.

Label the given figure as shown below:

From the diagram, it can be noticed that:

$\angle DOF=4x°$,$\angle AOB=64°$ and$\angle BOC=36°$

Step 3. Write the relation between the angles.

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

Therefore, the angles AOC and DOF are congruent angles. Therefore, the angles AOC and DOF have the same measure.

Step 4. Find the value of the angle AOC.

From the diagram it can be noticed that:

$\angle AOC=\angle AOB+\angle BOC$.

Therefore,

$$\begin{gathered} \begin{array}{c}\angle AOC=\angle AOB+\angle BOC\end{array} \\ =64°+36° \\ =100° \end{gathered}$$

Therefore, the measure of the angle AOC is 100°.

Step 3. Description of step.

Find the value of x by using the fact that the angles AOC and DOF have the same measure.

$\begin{array}{c}4x=100\\ x=\frac{100}{4}\\ x=25\end{array}$

Therefore, the value of x is 25.