Question

In Fig.8.2, $ABCD$ and $AEFG$ are two parallelograms. If $\angle C={55}^o$, determine $\angle F$.

• A. ${27.5}^o$
• B. ${55}^o$
• C. ${65}^o$
• D. ${45}^o$

Answer 1

Answer: (B)

$ABCD$ and $AEFG$ are two parallelograms sharing two sides $AD$ (or $AG$) and $AE$ (or $AE$) and the included angle.

$\angle C={55}^o$.

To find out- $\angle F$

Solution-

We have $\angle F=\angle A$ ......(opposite angles of a parallelogram).........(i)

Again $\angle A=\angle C$ ......(opposite angles of a parallelogram)...........(ii)

$\therefore \angle F=\angle C$ ......[From (i) and (ii)]

And $\angle C={55}^o$ .......(given)

$\Rightarrow \angle F={55}^o$