Question
$ABCD$ and $AEFG$ are two parallelograms. If $\angle\text{C}=55^\circ,$ determine $\angle\text{F}.$ 
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Answer
We have, $ABCD$ and $AEFG$ are two parallelograms and$\angle\text{C}=55^\circ.$ Since, $ABCD$ is a parallelogram, then opposite angles of a parallelogram are equal. $\angle\text{A}=\angle\text{C}=55^\circ\ ...(\text{i})$
Also, $AEFG$ is a parallelogram. $\therefore\ \angle\text{A}=\angle\text{F}=55^\circ$ [from eq.]
Also, $AEFG$ is a parallelogram. $\therefore\ \angle\text{A}=\angle\text{F}=55^\circ$ [from eq.]
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