Geometry Challenge

[rawi]

Solving with triangle solver of the Prime:
1st: Triangle BAC with BC = b (in Triangle Solver) = 1
BA = a = 1
Angle CBA = C = 70 degrees --> CA = c = 1.14715287
Angle BCA = A = 55 degrees
Angle BAC = B = 55 degrees
2nd: Triangle ACD with AC = a = 1.14715287
CD = b = 1
Angle ACD = C = 170 - 55 = 115 degrees
--> Side AD = c = 1.81261557
Angle BAD = 30 Degrees
Angle BAD + Angle BAC is the angle we searched: 85 degrees

Edit: Albert Chan pointed out in a private message that I had a typo concerning the length of CA. This had led to a wrong result. This is corrected now.