Golden 120° Symmetric Binary Tree
The red subtree whose trunk starts at the top of the main tree's trunk is a scaled version of the main tree. It has been rotated by $\theta$ and therefore the top edge of the main tree is also rotated by $\theta$ to become the top edge of the red subtree (and also scaled by $r$). Therefore angle $\beta = 180^\circ - \theta$.
We also have $\omega + \beta = \theta$ and so $\omega = \theta - \beta = 2\theta - 180^\circ$. Hence $\delta = 90^\circ - \omega = 270^\circ - 2\theta$. For the golden 120° tree, therefore, $\delta$ = 30° and $\beta$ = 60°.
(Note: These calculations for the angles work for any self-contacting symmetric binary tree with $90^\circ \le \theta \le 135^\circ$.)
