In the figure below, $ABCD$ is a parallelogram, where $AB$ is parallel to $CD$ and $AD$ is p

Question

In the figure below, $ABCD$ is a parallelogram, where $AB$ is parallel to $CD$ and $AD$ is parallel to $BC$. $E$ is on side $AD$. Produce $BE$ and $CD$, intersecting at $F$. Given that angle $BAE = 106^\circ$ and angle $BED = 143^\circ$, find the sizes of reflex angle $CBE$, angle $ABE$, angle $EFD$, angle $CDE$. Hence determine the type(s) of triangles $ABE$, $DEF$ and $CBF$, stating your reasons clearly.

Accepted Answer

(a) reflex $\angle CBE=323^\circ$ (b) $\angle ABE=37^\circ$ (c) $\angle EFD=37^\circ$ (d) $\angle CDE=74^\circ$ (e) $\triangle ABE$, $\triangle DEF$ and $\triangle CBF$ are isosceles

Triangles and Quadrilaterals

Triangles and Quadrilaterals

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