I'm studying for chem olympiad and have a question about a problem from a past year's test:

A pure sample of a monoprotic acid is dissolved in water.
The sample is titrated with sodium hydroxide solution.
At the point where 20.0 mL of the NaOH solution has
been added, the pH is 4.15. The phenolphthalein
endpoint of the titration is observed when 50.0 mL of
NaOH have been added. What is the pKa of the acid?


Here are my thoughts: 

Since pH = 4.15, pOH = 9.85 $\implies$ $[OH-] = 10^{-9.85}M$, which I think must also be the molarity of NaOH (this might be wrong). 

I don't understand otherwise how to solve this question. I have $K_a = \frac{ [H^+]^2}{[HA]}$ as concentration of protons equals concentration of conjugate base. I guess I have $[H^+] = 10^{-4.15}$ from the pH but I'm not sure if that's right since we added 20Ml of NaOH first, which would have changed the pH from what it originally was. 

How would I solve the question?