Question

In the given figure, $l||m||n$, If $x:y=5:4$, then the measure of angle z is :

• A. ${40}^{\circ }$
• B. ${50}^{\circ }$
• C. ${90}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

Answer: (D)

${80}^{\circ }$

Let $x=5a$ and $y=4a$

Now $\angle y+\angle 1={180}^{\circ }$ (Angle made on straight line $\left(n\right)$ are supplementary)

$\Rightarrow 4a+\angle 1={180}^{\circ }\Rightarrow \angle 1={180}^{\circ }-4a..........\left(i\right)$

Now $m||n$ and $t$ is transversal

$\therefore \angle x=\angle 1$ (Corresponding angles)

$\Rightarrow 5a=\angle 1\Rightarrow 5a={180}^{\circ }-4a\Rightarrow 9a={180}^{\circ }\Rightarrow a={20}^{\circ }$

Now $\angle y=4a=4\times {20}^{\circ }={80}^{\circ }$

Now $l||n$ and $t$ is transversal.

$\therefore \angle z=\angle y$ (Alternate angles)

$\Rightarrow \angle z={80}^{\circ }$