To prove indirectly that in a triangle ABC, if angle `A=135` degrees, then angle `B\ne 45` degrees, we first assume the negative of what we are trying to prove, then find some form of contradiction.
Angle `A=135` , and let angle `B=45` degrees.
Now we know that the sum of the angles in a triangle must add up to 180 degrees, so this means that
`A+B+C=180` now sub in the values
`135+45+C=180` solve for C
`C=180-180 = 0`
But if `C=0` degrees, then the triangle ABC cannot exist, since all angles must be greater than 0 degrees. We have a contradiction. Therefore the assumption that `B=45` degrees is incorrect.
Angle `B ne 45` degrees.