Question

Given that line $p||q$, calculate value of $x$ is

• A. ${137}^o$
• B. ${167}^o$
• C. ${124}^o$
• D. ${210}^o$

Answer 1

The correct option is A ${137}^o$

To find out the value of $x$, draw the line $r$ parallel to $p\text{and}q$ and split angle $x$ into two parts i.e. $z\text{and}w$.
Now,
$w={62}^o\left(\text{alternate int. angles theorem}\right)$
$z+{105}^o={180}^o\left(\text{Co interior angles theorem}\right)$
$z={180}^o-{105}^o$
$z={75}^o$
Now, we know that
$x=z+w$
$x={62}^o+{75}^o$
$x={137}^o$
Hence, option$\left(a\right)$ correct.