Question 159
Four points $A$, $B$, $C$ and $D$ in the plane are given such that $\overline{AB} = \overline{AC}$ and $\overline{AD} = \overline{BD}$. Let $E$ be a point on the line $AC$, such that $A$ lies between $E$ and $C$ (see picture).
If $\alpha = \angle BAE$ and $\beta = \angle ADB$ and $\alpha + \beta = 200^\circ$, find $\varphi = \angle CBD$.
If $\alpha = \angle BAE$ and $\beta = \angle ADB$ and $\alpha + \beta = 200^\circ$, find $\varphi = \angle CBD$.