Value of 'A'.

For a number to be divisible by $36,$ it must be divisible by both $9$ and $4.$ For our number to be divisible by $4, \text{A}$ must be divisible by $2.$ For our number to be divisible by $9,$ the digits must add up to a number divisible by $9,$ i.e. $4 + 3 + 4 + 0 + 2\times \text{A} = 18\ \text{or}\ 27$ Solving for $\text{A}$ gives $\text{A} = \frac{7}{2}\ \text{or}\ 8$ but $8$ is the only valid solution. Indeed, $8$ is divisible by $2$ as was required from the divisibility rule for $4$ listed above, so it is the correct answer.