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 58º.
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 58º.
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