check the picture below.
well, qm is a diameter chord, and lm is a tangent line, the point of tangency is always a right-angle, as you see it in darkred there.
well, first off, let's notice the inscribed angle of 27°, by the inscribed angle theorem, that means the intercepted arc is twice that much, as you see it there in green.
qm is a diameter, so the arcqpm is 180°, if we subtract the 54° from arcpq, we're left with the arcpm you see there of 126°.
by the tangent-chord angle theorem, ∡pmn is half of arcpm.