Question

Given that $l\parallel m\parallel n$ in the given figure.Find the value of $x$ and $y$

• A. $x={30}^o\text{and}y={150}^o$
• B. $x={40}^o\text{and}y={140}^o$
• C. $x={50}^o\text{and}y={130}^o$
• D. $x={60}^o\text{and}y={120}^o$

Answer 1

The correct option is A $x={30}^o\text{and}y={150}^o$

Given that line $l$ is parallel to line $n$,
$x+x={60}^o\left(\text{alternate interior angles theorem}\right)$
$2x={60}^o$
$x={30}^o$

Also, given that line $m$ is parallel to line $n$,
$y+x={180}^o\left(\text{co-interior angle theorem}\right)$
$y={180}^o-{30}^o$
$y={150}^o$