How many unique triangles can be made out of an obtuse angle and a 60 degree angle?

This is a strange question.  An obtuse angle is greater than 90 degrees.  So let's let one angle equal 60, another equal 91 and the last equal to 29 which all add up to 180.  That's one triangle.  Now you can design another triangle where the second angle is 91.001 degrees or 91.00003 degrees or 92.3745 degrees.  I think you can see that there's an infinite number of unique triangles.
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