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

It would violate the theorem of the sum of the interior angles of a triangle summing up to ${180}^{\circ}$.
We know that sum of all interior angles of a triangle is ${180}^{\circ}$. ---(1)
If we assume that one angle is right angle of ${90}^{\circ}$ and other angle be obtuse angle of $x$ such that $x > {90}^{\circ}$ .
Sum of the 2 angles is then $90 + x > {180}^{\circ}$.
Therefore our initial assumption of $x > {90}^{\circ}$ is incorrect and so the statement is false by the method of indirect proof.