To solve this problem, we need to find the angle \( x \) which subtends the arc in the sector OAPB of the circle. We know from the problem statement that the area of sector OAPB is \(\frac{5}{18}\) of the area of the entire circle.

The formula for the area of a sector of a circle is given by:

\(\frac{\theta}{360^\circ} \times \pi r^2\)

where \(\theta\) is the angle in degrees and \( r \) is the radius of the circle.

Since the area of sector OAPB is \(\frac{5}{18}\) of the total area, we have:

\(\frac{x}{360^\circ} \times \pi r^2 = \frac{5}{18} \times \pi r^2\)

By cancelling out \(\pi r^2\) from both sides, we get:

\(\frac{x}{360^\circ} = \frac{5}{18}\)

To find \( x \), we solve the equation:

\(x = \frac{5}{18} \times 360^\circ\)

Calculating the value:

\(x = \frac{5 \times 360^\circ}{18}\)

\(x = \frac{1800^\circ}{18}\)

\(x = 100^\circ\)

Thus, the value of \( x \) is 100 degrees.

This matches the correct answer from the options provided: 100 degrees.