A sign consists of square $ABCD$ and a triangular attachment $ABF$ outside the square, where&nbs

Question

A sign consists of square $ABCD$ and a triangular attachment $ABF$ outside the square, where $AB=AF$. Diagonal $AC$ and segment $DF$ intersect at $E$. It is given that $$\angle CAF=75^\circ.$$ Find $\angle BFA$. [3] Explain why triangle $ADF$ is isosceles. Hence find $\angle CDF$. [3] Find $\angle AEF$. [2] Give reasons for your answers.

Accepted Answer

(a) $75^\circ$ (b) $AD=AF$, so triangle $ADF$ is isosceles; $\angle CDF=60^\circ$. (c) $75^\circ$

Polygons - Properties of Special Quadrilaterals

Polygons - Properties of Special Quadrilaterals

Solution:

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