Question

Line $l$ is perpendicular to line $m$. What are the values of $x$ and $y$ ?

• A. $x={20}^o\text{and}y={35}^o$
• B. $x={25}^o\text{and}y={30}^o$
• C. $x={15}^o\text{and}y={40}^o$
• D. $x={10}^o\text{and}y={45}^o$

Answer 1

The correct option is D $x={10}^o\text{and}y={45}^o$

We know line $l$ is perpendicular to line $m$.
So, $x+y+{35}^o={90}^o$.

Here, non-adjacent angles between line $m$ and line $n$ are vertically opposite angle, hence these angles are equal.
$\Rightarrow y+{35}^o={80}^o$(vertically opposite angle)

So, $x+{80}^o={90}^o\Rightarrow x={10}^o$
And,
$y+35={80}^o$
$y={80}^o-{35}^o$
$y={45}^o$
Hence, Value of $x\text{and}y$ are ${10}^o\text{and}{45}^o$.
So, option $\left(d\right)$ correct.