Geometry Challenge

[Albert Chan]

Another vector solution, shape rotated, so that arg(vec(AD)) = ∠BAD

Code:

  D
   \
60° \  120°
----- C -----
 110°  \   
    70° \ 110°
   A-----B ------

vec(AD)
= vec(AB) + vec(BC) + vec(CD)
= cis(0°) + cis(110°) + cis(120°)
= cis(110°) + cis(60°)
= 2*cos((110°-60°)/2) * cis((110°+60°)/2)
= 2*cos(25°) * cis(85°)