Question

In the figure, $l||m$ and $p||q$. Find the value of $\angle x,\angle y,\angle w,\angle u$ and $\angle z$

• A. $x=75,y=75,z=105,w=75,u=75$
• B. $x=75,y=75,z=75,w=105,u=75$
• C. $x=75,y=105,z=105,w=75,u=75$
• D. $x=75,y=75,z=75,w=75,u=75$

Answer 1

The correct option is A $x=75,y=75,z=105,w=75,u=75$

$x+105={180}^{\circ }(\because x\&105arecointeriorangles)$

$x={75}^{\circ }$

$u=y\left(correspondingangles\right)$

$y=w\left(verticallyoppositeangles\right)$

$x=y\left(correspondingangles\right)$

$y+z={180}^{\circ }(sumofanglesonastraightline={180}^{\circ })$

$\because x={75}^{\circ }$

$x=y=u={75}^{\circ }=w$

$z=180-y=180-75={105}^{\circ }$

$\therefore x=y=w=u={75}^{\circ }$

$andz={105}^{\circ }$