How did I get this wrong?

69 degrees (aha, perfecto lol)

Step-by-step explanation:

I don't know how you got 50 degrees but here's my explanation of how I got 69 degrees.

Line DC is parallel to Line AB. That means the angle between the bisector BC has to be supplementary, meaning, they have to equal 180 degrees. Since we know that angle-DCB is 65 degrees, the angle adjacent has to equal 180-65. But we can't split them between two parts.

So, the opposite angle is inside the triangle which equals 65 degrees, also. Opposite angles have the same angle measure when two parallel line gets bisected. So we know the two-angle measure for the triangle. Angle-ACB is also located in the triangle, thus, we can solve it with simple rules.

When you add up all the angle measurements in a triangle, it has to equal 180 degrees. We already know two of them. 180 - (65 + 46) = angle-ACB. With simple algebra or the use of a calculator, we get the result of 69 degrees.

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)