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

Question

In the figure below, $ABCD$ is a parallelogram, where $AB$ is parallel to $CD$ and $BC$ is parallel to $AD$. $E$ and $F$ lie on $AD$ and $CD$ produced respectively and $BF$ intersects $AD$ at $G$. Given that angle $ABG = 24^\circ$, angle $BAG = 58^\circ$, angle $CED = 98^\circ$. Find the sizes of angle $DFG$, angle $CDG$, angle $BGD$. Hence deduce the relationship between line segments $BF$ and $CE$.

Accepted Answer

(i) $24^\circ$ (ii) $122^\circ$ (iii) $82^\circ$ Hence $BF\parallel CE$.

Angles Formed by Two Parallel Lines and a Transversal

Angles Formed by Two Parallel Lines and a Transversal

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