Question
In the given figure, $ABCD$ and $AEFG$ are two parallelograms. If $\angle\text{C}= 58^\circ,$ find $\angle\text{F}.$ 
✓
Answer
$ABCD$ and $AEFG$ are two parallelograms as shown below:
Since $ABCD$ is a parallelogram, with $\angle\text{C}=58^\circ$
We know that the opposite angles of a parallelogram are equal.
Therefore, $\angle\text{A}=\angle\text{C}$ $\angle\text{A}= 58^\circ,$
Similarly, $AEFG$ is a parallelogram, with $\angle\text{A}= 58^\circ,$
We know that the opposite angles of a parallelogram are equal.
Therefore, $\angle\text{F}=\angle\text{C}$
$\angle\text{F}= 58^\circ$
Hence, the required measure for $\angle\text{F}$ is $58^\circ $.
Since $ABCD$ is a parallelogram, with $\angle\text{C}=58^\circ$
We know that the opposite angles of a parallelogram are equal.
Therefore, $\angle\text{A}=\angle\text{C}$ $\angle\text{A}= 58^\circ,$
Similarly, $AEFG$ is a parallelogram, with $\angle\text{A}= 58^\circ,$
We know that the opposite angles of a parallelogram are equal.
Therefore, $\angle\text{F}=\angle\text{C}$
$\angle\text{F}= 58^\circ$
Hence, the required measure for $\angle\text{F}$ is $58^\circ $.
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