Question

In the given figure $PQ$ ∥ $XY$ ∥ $RS$. Also, $y$ : $z$ = $4$ : $5$, then the values of $\angle x$, $\angle y$ and $\angle z$ are (respectively).

• A. ${80}^{\circ },{80}^{\circ },{100}^{\circ }$
• B. ${100}^{\circ },{80}^{\circ },{100}^{\circ }$
• C. ${80}^{\circ },{100}^{\circ },{100}^{\circ }$

Answer 1

The correct option is B ${100}^{\circ },{80}^{\circ },{100}^{\circ }$

Let the common ratio be $a$
Then $y=4a$ and $z=5a$
Also, $\angle z$ = $\angle m$ (Alternate interior angles)
Since, $z=5a$,
$\angle m=5a$ [$RS$ ∥ $XY$ cut by transversal $t$]

Now, $\angle m$ = $\angle$ x (Corresponding angles)
Since, $\angle m=5a$

$\therefore \angle x=5a$ [$PQ$ ∥ $RS$ cut by transversal $AB$]

$\angle x+\angle y={180}^{\circ }$ (Co-interior angles)
$5a+4a={180}^{\circ }$
$9a={180}^{\circ }$
$a=\frac{180}{9}$
$a={20}^{\circ }$

Since, $y=4a$
$\therefore y=4\times 20$
$y={80}^{\circ }$

$z=5a$
$\therefore z=5\times 20$
$z={100}^{\circ }$

$x=5a$
$\therefore x=5\times 20$
$x=100°$