Question

In the above figure, ACDF, ABEF and BCDE are parallelograms. Analyse the given figure and choose the correct option(s).

• A. $\angle AFE=x$
• B. $\angle FBD=x+y$
• C. $\angle BCD=z$
• D. $\angle CDG=x+y$

Answer 1

Answer: (B), (C)

The correct options are
B

$\angle FBD=x+y$

C

$\angle BCD=z$

Since ABEF is a parallelogram, so AF || BE and BF is the transversal.
$\therefore \angle AFB=\angle FBE=x$
$\text{[Alternate angles]}$

Also, since BCED is a parallelogram,
BE || CD and BD is the transversal.
$\therefore \angle CDB=\angle EDB=y$
$\text{[Alternate angles]}$

Now,
$\angle FBD=\angle FBE+\angle EBD$
$\angle FBD=x+y$

And,
$\angle AFE=\angle BED$
$\text{[Corresponding angles]}$
$\therefore \angle AFE=z$

$\angle BED=\angle BCD=z$
$\text{[opposite angles of a parallelogram]}$

$\angle CDG+\angle BCD=\angle EBD+\angle BED$
$\text{[Sum of opposite interior angles is}\text{equal to exterior angle of a triangle]}$

$\Rightarrow \angle CDG=y+z-y$
$\Rightarrow \angle CDG=z$