Question

The lines $UX$ and $WY$ intersects at point $V$ and $UY$ and $WX$ are parallel lines, then the length of $WY$ is:

• A. $8$
• B. $9$
• C. $10$
• D. $12$

Answer 1

Answer: (A)

$8$

Given: line $WX\parallel$ line $UY$

$\therefore \angle W=\angle Y$ .....alternate angles

And, $\angle X=\angle U$ .....alternate angles

$\therefore △VWX\sim △VYU$ ...A.A test of similarity

$\therefore \frac{VW}{VY}=\frac{VX}{VU}$ ....C.S.S.T

$\therefore \frac{VW}{6}=\frac{3}{9}$

$VW=2$ units

Now, $WY=VW+VY=2+6=8$ units