# Given: In triangle ABC, <A=135 degrees. Prove: <B `!=` 45 degrees. (Write an indirect proof.) (An image is not given)

*print*Print*list*Cite

### 1 Answer

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.**