Question

Calculate the value of $x$ in the given figure if $p$ is parallel to $q$.

• A. ${98}^o$
• B. ${262}^o$
• C. ${88}^o$
• D. ${108}^o$

Answer 1

The correct option is A ${98}^o$

First let's draw the line $r$ parallel to lines $p\text{and}q$ as in the figure below.

let one angle is $\alpha$ and other be $\beta$ as shown in the figure.

Now, in the figure we can see that,
$\alpha ={135}^o(\because \text{equal corresponding angles on p \& r})$
Also,
$\beta ={127}^o(\because \text{equal corresponding angles on r \& q})$
Now,
$x+\alpha +\beta ={360}^o$
$x+{135}^o+{127}^o={360}^o$
$x+{262}^o={360}^o$
$x={360}^o-{262}^o$
$x={98}^o$
Hence, option $\left(a\right)$ correct.