考慮 $\Delta BCE$ 及 $\Delta DCF$。
$\begin{array}{rcll}
BC & = & DC & \text{(菱形性質)}\\
\angle CBE & = & \angle CDF & \text{(菱形性質)} \\
AD & = & AD & \text{(菱形性質)} \\
BE & = & AB – AE \\
& = & AD – AF & \text{(已知)} \\
& = & DF
\end{array}$
所以,$\Delta BCE \cong \Delta DCF\ \text{(S.A.S.)}$。
由此,可得 $CE = CF\ \text{($\cong \Delta$ 的對應邊)}$。
由於 $AE = AF$ 及 $CE = CF$,$AECF$ 為一鳶形。所以,$\angle AEC = \angle AFC$。由此,可得
$\begin{array}{rcll}
\angle AEC + \angle AFC + \angle EAF + \angle ECF & = & 360^\circ & \text{(多邊形的內角和)} \\
2\angle AEC & = & 360^\circ – 42^\circ – 110^\circ \\
\angle AEC & = & 104^\circ
\end{array}$
所以,可得
$\begin{array}{rcll}
\angle BEC & = & 180^\circ – \angle AEC & \text{(直線上的鄰角)} \\
\angle BEC & = & 180^\circ – 104^\circ \\
\angle BEC & = & 76^\circ
\end{array}$