I have a rectangle in landscape orientation and I want to rotate using the upper left corner as the center of rotation. I want to snap the bottom edge of the rectangle to an intersection of two lines below and right of the rectangle. I am totally stumped on how to do this.

After selecting the rotation center, I am prompted to select reference point and this is where the problem begins, I don't know where on the bottom edge the reference point is. If I select the same point as the rotation center it asks for an angle, again I don't know this as I want the bottom edge of the rectangle to snap to an intersection of two lines.

You have to do some auxiliary construction. Draw a circle around the rotation center with a radius going through the intersection of the two lines. Where this intersects the bottom edge of the rectangle there is the reference point.