In triangle ABC, angle C = 90 degrees and angle B = 35 degrees, CD is the height. Find the angles of the ACD triangle.

Because the sum of the angles of triangle ABC is 180 degrees, then angle (A) = 180 – angle (B) – angle (C) = 180 – 35 – 90 = 55 degrees.
angle (A) in triangle ACD is equal to angle (A) in triangle ABC, because point D lies on AB.
the angle (D) in the ACD triangle is 90, because CD – height.
Because the sum of the angles of the triangle ACD is 180 degrees, then the angle (C) = 180 – angle (A) – angle (D) = 180 – 55 – 90 = 35 degrees.
Answer: Angle (A) = 55 degrees, Angle (C) = 35 degrees, Angle (D) = 90 degrees.