POI is a bent molecule similar to water. How are the two molecules different it terms of bond angles and what causes this?
Does this mean that:
  
  
    Due to the extra lone pair $\color{red}{\text{it}}$ $\color{limegreen}{\text{creates less resistance}}$ resulting in $\color{blue}{\text{a greater angle}}$?
  


More like:

Due to the extra lone pair $\color{red}{\text{in } \ce{H2O} \text{ the pendant atoms}}$ $\color{limegreen}{\text{experience more repulsion}}$ resulting in $\color{blue}{\text{a smaller angle}}$ $\color{magenta}{\text{compared to }\ce{POI}}$? 




  Also, does it having three different elements in the equation do anything?


No, I think the three different elements in the question were there to evaluate if you were:


estute to the fact that oxygen forms a double bond thus
phosphorous has 1 unbonded pair of electrons (not 2) and
if the double bond would hang you up in obtaining an answer.