Question

In figure, if $\frac{y}{x}=5$ and $\frac{z}{x}=4$, then the value of $x$ is

• A. $8^{\circ }$
• B. ${18}^{\circ }$
• C. ${15}^{\circ }$
• D. ${12}^{\circ }$

Answer 1

The correct option is B ${18}^{\circ }$



Given : $\frac{y}{x}=5$ and $\frac{z}{x}=4$

From the figure,
$x,y$ and $z$ are on straight line
$\therefore x+y+z={180}^{\circ }.....\left(i\right)$

Since, $\frac{y}{x}=5$
$y=5x.....\left(ii\right)$

Also, $\frac{z}{x}=4$
$z=4x.....\left(iii\right)$

Substituting $\left(ii\right)$ and $\left(iii\right)$ in $\left(i\right)$, we get,

$x+5x+4x={180}^{\circ }$
$10x={180}^{\circ }$
$x={18}^{\circ }$

Hence, option (b) is correct.