An obtuse triangle has exactly one obtuse angle.

Explanation:

• An obtuse angle is an angle greater than 90° but less than 180°.
• In a triangle, the sum of all three angles is always 180°.
• If a triangle had two obtuse angles, their sum would be greater than 180°, which is impossible.
• Therefore, an obtuse triangle can only have one angle greater than 90°, and the other two angles must be acute (less than 90°).

So, the number of obtuse angles in an obtuse triangle is one.