An obtuse triangle has exactly one obtuse angle.

The reason is:

  • The three interior angles of any triangle must add up to 180 degrees.
  • An obtuse angle is greater than 90 degrees.
  • If you tried to have two angles both greater than 90 degrees, their sum alone would already be more than 180 degrees, which is impossible for a triangle.

So in an obtuse triangle:

  • 1 angle is obtuse (greater than 90°).
  • The other 2 angles are acute (each less than 90°).

A quick way to remember it: a triangle can be “obtuse” in only one corner at a time.