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To solve for the unknown angle measures, we can set up an equation by adding the measures of the three angles and equating it to 180 degrees.
The measure of angle KLM is given as (x+30) degrees.
The measure of angle MAN is given as 60 degrees.
The measure of angle NLP is given as (2x) degrees.
Adding up the measures of the angles:
(x+30) + 60 + (2x) = 180
Simplifying the equation:
3x + 90 = 180
This equation can be solved to find the value of x.