We are given a right-angled triangle MNK with a right angle N, that is, an angle MNK = 90 degrees. It is known that the height NT forms a right angle with the hypotenuse MK, since the height is a perpendicular. Hence the angle NTK = 90 degrees. Find the angle NKT in the triangle MNK, based on the theorem on the sum of the angles of the triangle:
180 – 90 – 12 = 72 degrees.
Now, using the same theorem, we find the unknown angle TNK in the triangle NTK:
180 – 90 – 72 = 12 degrees.
Answer: TNK angle = 12 degrees.
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