Question

In the above figure, ACDF, ABEF, and BCDE are parallelograms. Which of the following statement is wrong regarding the given figure?

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

Answer 1

The correct option is C $x+y=z$


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

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

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

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

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

$\angle BED=\angle CDG=z$
$\text{[Corresponding angles of a parallelogram]}$

$\text{Therefore, Option c is wrong.}$