How many obtuse angles does a triangle have?

A triangle can have a maximum of ##1## obtuse angle.

Any triangle must have interior angles that add up to ##180^@##. An obtuse angle is an angle greater than ##90^@## but less than ##180^@##.

If you had an angle that was ##91^@##. The other ##2## angles would have to be acute. This is because the other angles would take up ##180^@-91^@=89^@## of the triangle. Since ##89^@## is less than ##90^@##, this means the other ##2## angles must both be acute. You are left with ##1## obtuse angle.