How many triangles exist with the given angle measures? 32°, 51°, 97°

For each triangle sum of it's angles must add to 180°.
We need to check if these angles satisfy that condition:
32°+51°+97°=180°

They do satisfy. Now we check if any angle has value that is not possible.
32° and 51° angles are OK.
97° angle is also OK. It is obtuse angle.

For each angle measures exactly one triangle exists. In this example we have an obtuse-angle triangle.