As the holes are equidistant on both the plates, they form pentagon and square on their respective plate (as shown in the figure)

Lets consider two circular plates as below:
Plate1: Consider holes A & B are on Pentagon in plate1
Plate2: Consider holes P & Q are on square in plate2

Its given that two plates are kept over other and two of their holes are coinciding. Lets assume holes A & P are coinciding.
From the diagram you can see, holes B & Q can be aligned with minimum rotation. i.e. we need to find out <BOQ = x =?

Central angle formed by two vertices of pentagon i.e. \(<AOB = y = \frac{360}{5} = 72\)
Central angle formed by two vertices of square i.e. \(<POQ = \frac{360}{4} = 90\)

\(<AOB + <BOQ = <AOQ\)
i.e. \(y + x = 90\)
i.e. \(72 + x = 90\)
Resolve to \(x = 18\)

Hence choice (C) is the answer