Question

If line $a$ is parallel to $b$, line $p$ is parallel to line $DF$ and line $q$ is perpendicular to both parallel lines $a\&b$.
What is the value of $x$ in the figure given below ?

• A. ${40}^o$
• B. ${80}^o$
• C. ${50}^o$
• D. ${45}^o$

Answer 1

The correct option is C ${50}^o$

In the above figure,
$y={40}^o(\because \text{Corresponding angles})$
$z+y={90}^o(\because q\text{is perpendicular to}a\&b)$
$z={90}^o-{40}^o$
$z={50}^o$
Now,
$z=w(\because \text{Corresponding angles})$
$w={50}^o$
Also,
$x=w(\because \text{Corresponding angles})$
So, $x={50}^o$
Hence, option$\left(c\right)$ is correct.