Side AB of triangle ABC is extended beyond point B. Point D is marked on the continuation so that BC = BD.

Side AB of triangle ABC is extended beyond point B. Point D is marked on the continuation so that BC = BD. Find the ACD angle if ∠ACB = 60 ° and ∠ABC = 50 °.

1. First, let’s find the DBC angle. It is an angle adjacent to the ABC angle, the degree measure of which is known to us. The sum of adjacent angles is 180 degrees. Let’s find the angle of the DBC: 180 – 50 = 130 degrees.
2. Now we will consider the DVS triangle. It is isosceles (BC = BD given). Knowing that the angles at the base are equal and the sum of the angles of the triangle = 180 degrees, we can find the angle DCB: (180 – 130) / 2 = 25 degrees.
3. The angle ACD can be calculated by adding the angles ACB and BCD, the degree measures of which we now know. Hence the angle ACD = 60 + 25 = 85 degrees.
Answer: ACD angle is 85 degrees.