The following pentagon is composed by $10$ discs. Each disc must be filled with one number. The allowed numbers to be used are the first $10$ even positive numbers. The sum of the numbers to be placed in each side of the pentagon must be the same and the maximum posible. Find the sum of the numbers adjacent to the discs filled with the numbers $2$ and $18$.
The figure is shown below:
The alternatives given are:
$\begin{array}{ll} 1.&54\\ 2.&60\\ 3.&50\\ 4.&64\\ \end{array}$
I tried several ways to fill up this pentagon but none did really came up with a clear solution. Does it exist a method, strategy or something that can be used in an effective manner to solve this riddle?. I'd appreciate someone could help me with this. I'm stuck at the very beginning hence I can't offer more. Since I believe this would require the use of maths, please try to include some visual aid and the most detailed way to solve this problem as I mentioned I don't know what can be done to solve this.