Question

In the figure, $ABCD$ and $AEFG$ are parallelograms. If $\angle C={55}^{\circ },$ what is the measure of $\angle F?$

Answer 1

Given: $\angle C={55}^{\circ }$

In the parallelogram ABCD, we have​

$\angle DAB=\angle DCB....\left(i\right)$ (Opposite angles of a parallelogram)​

Similarly in parallelogram $\angle GAE=\angle GFE....\left(ii\right)$

​ From $\left(i\right)$ and $\left(ii\right),$​ we have

$\angle DCB=\angle GFE={55}^{\circ }$ $(\because \angle DCB=\angle C={55}^{\circ })$AEFG,​

Hence $\angle F={55}^{\circ }$