Question

In the adjoining figure, parallel lines are shown with similar markings. Find $\angle x$, if $\angle x=5\angle y$.

• A. ${30}^o$
• B. ${60}^o$
• C. ${150}^o$
• D. ${170}^o$

Answer 1

The correct option is C ${150}^o$

REF.Image

as $l_1,l_2,l_3,l_4$

are $\parallel$ to each

other &

$r_1,r_2,r_3,r_4$

$\parallel$ to each other,

So, $\angle ABC=$

$\angle DFE$

$\therefore \angle DFC=x^{\circ }$

In $\angle DFE+\angle EFG={180}^{\circ }$ (Linear pair)

$\angle x+\angle y={180}^{\circ }$

$5\angle y+\angle y={180}^{\circ }$ $(\because \angle x-5\angle y)$

$\angle y={30}^{\circ }$

$\therefore \angle x=5\times {30}^{\circ }$

$\angle x={150}^{\circ }$