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 $CD$ and $F$ is on $BE$ such that $AE = EF$. Given that angle $AEF = 48^\circ$, angle $BAF = 18^\circ$ and angle $ADE = 62^\circ$, find the sizes of angle $FBA$, angle $CBE$, angle $DAE$, angle $CEB$. Hence, determine the type of triangle $ABE$, stating your reason clearly.

Accepted Answer

(a) $\angle FBA=48^\circ$ (b) $\angle CBE=14^\circ$ (c) $\angle DAE=34^\circ$ (d) $\angle CEB=48^\circ$ (e) $\triangle ABE$ is isosceles

Triangles and Quadrilaterals

Triangles and Quadrilaterals

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