In the figure below, $ABCD$ and $ACEF$ are rhombuses, where $AE$ intersects $CD$ and $CF$

Question

In the figure below, $ABCD$ and $ACEF$ are rhombuses, where $AE$ intersects $CD$ and $CF$ at $M$ and $N$, respectively. Given that angle $ACB = 26^\circ$, find the sizes of: angle $CEN$, angle $CDF$, angle $DMN$, angle $MCN$. Suppose now, given that angle $ACB \neq 26^\circ$ and triangle $CMN$ is a right-angled isosceles triangle, where $CN = MN$. Find the new size of angle $ACB$.

Accepted Answer

(a) $13^\circ$ (b) $52^\circ$ (c) $141^\circ$ (d) $51^\circ$ (e) $30^\circ$

Triangles, Quadrilaterals

Triangles, Quadrilaterals

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