The sum of the measures of the triangle is 15x+1+4x-1+6x+5 = 25x+5. 25x+5 is equal to 180 degrees because the interior angles of a triangle always sum to 180 degrees. Solving for x gives us the following:
25x+5 = 180
25x = 175
x = 7.
Substituting x=7 into all the expressions gives us the angle measures, in degrees: 106, 27, and 47. Since the triangle has a obtuse angle, it is an obtuse triangle.
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