On hypotenuse AB of right triangle ABC, D is the point for which CB = BD. If angle B measures 40 degrees, find the measure of angle ACD.
In triangle CBD, angle CBD = 40°
And since CB = BD then angle BDC = angle BCD = [ 180 - 40] / 2 = 140 / 2 = 70°
And angle BCA = angle BCD + angle ACD......
And angle BCA = 90 and angle BCD = 70
90 = 70 + angle ACD subtract 70 from both sides
20° = angle ACD