You'd use 45degree angles. If that tile was installed correctly, you could follow right along the grout line starting at the bottom of the photo [though that would probably require modifying your 6 inches to the side idea, it would probably look best].

I picture that you want the front left corner of the countertop to be clipped at a 45-degree angle? Sort of along the grout line?

If so, I wouldn't recess the entire depth of the tray cebinet depth. I'd clip the face of the tray cabinet as well so it's full depth next to the dishwasher and less deep a the cabinet end panel.

Sumptin' like this is what I'm picturing, which is a 3-minute doctoring drill with photoshop:

For the geomerty lesson, for any right triangle (a triangle with a 90-degree corner in it), the length of the hypoteneuse (the longest side) is equal to the sum of the squares of the other two sides.

If you want to lose 6" off the front and off the left edge, then 36 plus 36 = 72. The square root of 72 should be just a bit less than 8.5", so the length of the clipped corner would be about 8.5".

Since this is also a right isosceles triangle (a triangle that has two sides the same length and also has a right angle) then you could also find the length of the hypoteneuse by multiplying the length of the leg by the square root of 2.

Again, 6" times 1.41 should come close to equaling 8.5".

Mongo

We got rid of the countertop....but I could still do that, I guess! Would I still need to cut about 4" off the depth of the cabinet to allow for the clip?

Thanks, Mongo... I'd love to do it that way (rather than cutting back the whole cabinet...) but.... we would then have to have a new door made. Not sure if my carpenter could do that to match the others....Also, wouldn't it be hard to cut the front of the cabinet at that angle? Maybe not...but what about the door?

I'll send my daughter to you for help with her math homework!

Thanks ~

Any carpenter or cabinetmaker should ba able to make that adjustment.

One thing to consider is the flooring. If the flooring does not extend under the cabinets, have you thought about how you'll patch the floor?

He could also make a single door that would cover both facets of the opening. Not tough to do at all. Just cut two panels and bevel the two to-be-mated edges at a 22-1/2 degree angle. Then biscuit them together so you end up with a door with a 45 degree break in it.

It would work quite nicely.

Regarding my geometry, I did the math correctly but left out part of the pythagorean theorem when I wrote the words.

For a right triangle, the length of the hypoteneuse is equal to the square root of the sum of the squares of the other two sides.

I'll help your daughter with math if she'll help me with photoshop!

Mongo

Thanks, Mongo...I'll run this by him tomorrow... I'd like that look better but was sure it would be more of a challenge...and, therefore, more of an expense! Do you think it would be harder to cut it off at an angle than cutting off the back?

The floor isn't finished yet, so when the hardwood floor installers come back to sand and finish later (after everything else is in) they could put in a couple more strips of wood. (We've had hardwood added since the picture was taken)

Appreciate your taking the time to help. I'll let you know what we end up doing...