In triangle ABC, angle C is 65 degrees, AB = BC. AH is the height of the triangle. Find the value of the angle BAH.

Consider a triangle ABC: since it is isosceles, then angle A = angle C = 65 degrees, now we find angle B = 180 degrees – (angle A + angle C) = 180 – (65 + 65) = 50 degrees.

Next, consider the triangle ABH:

since AH is the height, the angle AHB = 90 degrees (by property). The sum of all the angles of the triangle is 180 degrees, then we get the angle BAH = 180 degrees – (angle ABH + angle AHB) = 180 – (50 + 90) = 180 – 140 = 40.

Answer: BAH is 40 degrees.