Why can an obtuse triangle have only one obtuse angle?

Hint

Use the triangle Angle Sum Theorem. Or try fitting two elephants into a one-bedroom flat.

Answer

Let's see what happens if we say that ∠1, ∠2, and ∠3 make up the interior angles of a triangle and both ∠1 and ∠2 are obtuse. Obtuse angles are greater than 90°, so just adding the measures of ∠1 and ∠2 would be greater than 180. That means ∠3 would have to be negative and we can't have negative angles.