How many obtuse interior angles are in an obtuse triangle?
By definition, an obtuse triangle contains one obtuse interior angle. It cannot contain more than one because an obtuse angle has measure greater than 90 degrees and the sum of all the interior angles in any triangle is 180 degrees. Thus, there is $\boxed{1}$ obtuse angle.
1
Level 1
Prealgebra
Problem: How many obtuse interior angles are in an obtuse triangle?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>An obtuse triangle is defined as a triangle that has one angle greater than 90 degrees. This means that the obtuse angle is the largest angle in the triangle. The sum of the interior angles in any triangle is always 180 degrees. 

If one angle is obtuse, it must be greater than 90 degrees. Let’s denote the obtuse angle as A, where A > 90 degrees. The remaining two angles, B and C, must then be acute angles, meaning they are each less than 90 degrees. 

Since the sum of the angles in the triangle is 180 degrees, we can express this as:
A + B + C = 180 degrees.

Given that A > 90 degrees, we can infer that:
B + C = 180 degrees - A.

Since A is greater than 90 degrees, the sum of B and C must be less than 90 degrees. This implies that both B and C must be less than 90 degrees, confirming that they are acute angles.

Thus, in an obtuse triangle, there can only be one angle that is obtuse, while the other two angles must be acute. Therefore, the conclusion is that there is exactly one obtuse interior angle in an obtuse triangle. 

The final answer is 1.<|END_OF_LATENT|> The final answer is $1$.