What is the corollary to the triangle sum theorem?

The corollary to the triangle sum theorem is the law of cosines, better known as the Pythagorean theorem. This theorem is often used in calculus courses.

The theorem states that the sum of all three angles in a triangle must equal 180 degrees. A corollary of that theorem would then have to mean that a triangle can include only one 90 degree angle or one obtuse angle. This must be true since a triangle with more than one 90 degree angle or more than one obtuse angle would not meet the requirements because the sum of those three angles would be larger than 180 degrees.