To determine the volume of the acid needed in the reaction, we first have to know the reaction involved in the process. Since it is a neutralization reaction, then it should produce a salt and water. The reaction would be:
HCl + KOH = KCl + H2O
We use this reaction to relate the substances. We calculate as follows:
0.137 M KOH (.02867 L solution ) = 3.92779x10^-3 mol KOH
3.92779x10^-3 mol KOH ( 1 mol HCl / 1 mol KOH ) = 3.92779x10^-3 mol HCl
Volume of HCl = 3.92779x10^-3 mol HCl / 0.117 M HCl
= 0.03357 L HCl or 33.57 mL HCl needed