In triangle MNK, the heights of MP and NF intersect at point A. Angle MNK = 64 degrees

In triangle MNK, the heights of MP and NF intersect at point A. Angle MNK = 64 degrees, angle MKN = 78 degrees Find the angle POF

The heights MP and NF intersect at point O. Consider the FOPK quadrilateral: the angles OPK and OFK are equal to 90 degrees, since MP and NF are perpendicular to the segments NK and MK, respectively, the angle MKN = 78 degrees (by condition).
By the theorem on the sum of the angles of a quadrangle:
OPK angle + MKN angle + OFK angle + POF angle = 360 degrees;
90 + 78 + 90 + POF angle = 360;
angle POF = 360 – 90 – 90 – 78 = 102 (degrees).
Answer: POF angle = 102 degrees.