Question

Why can't a triangle have a right angle and an obtuse angle?

Answer 1

It would violate the theorem of the sum of the interior angles of a triangle summing up to `180^@`.

Explanation:

We know that sum of all interior angles of a triangle is `180^@`. ---(1)
If we assume that one angle is right angle of `90^@` and other angle be obtuse angle of `x` such that `x>90^@` .
Sum of the 2 angles is then `90 + x >180^@`.
It cannot be possible due to equation (1). (Contradiction).
Therefore our initial assumption of `x>90^@` is incorrect and so the statement is false by the method of indirect proof.