3261.11 – Quadrilateral BCDF is a Rhombus

Given: Quadrilateral $\square BCDF$ is a rhombus. Point $A$ is on the extension of the line $BC$ past $B$ and is positioned so that $AF$ is parallel to the diagonal $BD$ and meets the extension of $CD$ at $E$. Angle $\angle ACD$ measures $100^\circ$.

Find the measure of angle $\angle CEA$.

Solution

$\angle B_1$ and $\angle D_1$ are equal to $40^\circ$. $\angle AEC$ equals $\angle B_1$ by the theorem on corresponding angles.