[how would I create a sloped roof]

Hello all, 

I am currently working on a house and have come across a problem that I can't solve. 

I am looking to create a sloped roof that sits flush to the story below. I Have managed to create the slope however the problem is the corners of the roof stick out and are not flush (pictures 1 & 2 below).

I am aiming to achieve a result like this (illustrations 3 & 4 below).

I achieved the result I have at the moment by;

- lofting between 2 poly lines

- create a cut-out of the roof

- subtracting solids 

Any help would be much appreciated

Regards,

Felix