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

1 Answer

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.