In the figure below, $ABCD$ is a kite, where the diagonals $AC, BD$ intersect at $O$. $E$ is

Question

In the figure below, $ABCD$ is a kite, where the diagonals $AC, BD$ intersect at $O$. $E$ is a point on $BD$, such that $AECD$ is a rhombus. Given that angle $EAO = 33^\circ$, angle $BCF = 87^\circ$, where $F$ is a point on the extension of $DC$, find the sizes of angle $ADO$, angle $AEC$, angle $DCE$, angle $BCE$. Hence determine the type of triangle $ABC$, stating your reasons clearly.

Accepted Answer

(a) $\angle ADO=57^\circ$ (b) $\angle AEC=114^\circ$ (c) $\angle DCE=66^\circ$ (d) $\angle BCE=27^\circ$ (e) $\triangle ABC$ is equilateral

Polygons

Polygons

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