In the triangle ABC AC = BC, AD is the height, the angle BAD is 14 °. Find the corner C.

Find the angle ABD in triangle ABD:
angle BAD + angle ABD + angle BDA = 180 degrees;
14 + angle ABD + 90 = 180;
angle ABD = 76 degrees.
AC = BC, then ABC is isosceles, angle ABD = angle BAC = angle B = angle A = 76 degrees.
Find angle C:
angle A + angle B + angle C = 180 degrees;
76 + 76 + angle C = 180;
angle C = 180 – 152;
angle C = 28 degrees.
Answer: angle C = 28 degrees.