Question

Find the values of $x$ and $y$ in the given figure ?

• A. $x={60}^o$ and $y={90}^o$
• B. $x={120}^o$ and $y={90}^o$
• C. $x={90}^o$ and $y={60}^o$
• D. $x={90}^o$ and $y={120}^o$

Answer 1

The correct option is D $x={90}^o$ and $y={120}^o$

By using exterior angle sum property,
we know that sum of all exterior angles of polygon is equal to ${360}^o$. So,
$x+x-{50}^o+x-{40}^o+x+x={360}^o$
$5x-{90}^o={360}^o$
$5x={360}^o+{90}^o$
$5x={450}^o$
$x=\frac{{450}^o}{5}$
$x={90}^o$

Now, $y-{30}^o$ and $x$ makes linear pair, So
$y-{30}^o+x={180}^o$
$y-{30}^o+{90}^o={180}^o$
$y={180}^o-{90}^o+{30}^o$
$y={120}^o$

Hence, value of $x$ and $y$ are ${90}^o$ and ${120}^o$ respectively.

So, option $\left(d\right)$ correct.