In the diagram, $BCDE$ is a quadrilateral and $\Delta ABE$ is an isosceles triangle. $ED$ is p

Question

In the diagram, $BCDE$ is a quadrilateral and $\Delta ABE$ is an isosceles triangle. $ED$ is parallel to $BC$ and $EB$ is parallel to $DC$, $ED=BC$ and $EB=DC$. Given that $\angle AEB=82{}^\circ $ and $\angle BCE=26{}^\circ $, state the special name of the quadrilateral $BCDE$, find the values of $x$, of $y$ and of $z$. State all reasons in your workings.

Accepted Answer

(a) Parallelogram; (b) x=49, y=23, z=26.

Geometry Problem Involving Parallel Lines and Isosceles Triangle

Geometry Problem Involving Parallel Lines and Isosceles Triangle

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