What is the definition or theorem if ray nm perpendicular to line gh, then angle nmp and angle pnh are complementary?

I'm not entirely sure where you have p situated, but I 'think' I know from the context of the question.
That would be one definition of complementary angles. We're told that nm is perp to gh so angle nmh is right by definition of perp. Since measure nmp + measure pnh = nmh the two are comp.

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