For any triangle, sum of the measures of all three angles is 180 degrees. Accordingly sum of the measures of angles K,L and M will be 180. That means (2x+2) + (3x+5) + (x-7) = 180

Or, 6x= 180

Hence x= 30.

This gives Angle K= 2x+2 = 62 degrees

Angle L= 3x+5= 95 degrees

And Angle M= x-7= 23 degrees

These calculations show that all the angles are different and one of them is greater than 90 degrees. Hence Triangle KLM is an Obtuse Triangle.

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