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