Question

In the given figure, if $\frac{y}{x}=5$ and $\frac{z}{x}=4$, then the value of $x^{\circ }$ is
(a) $8^{\circ }$
(b) ${18}^{\circ }$
(c) ${12}^{\circ }$
(d) ${15}^{\circ }$

Answer 1

In the given figure, we have $x^{\circ },y^{\circ }$ and $z^{\circ }$ forming a linear pair, therefore these angles must be supplementary.

That is,

$x^{\circ }+y^{\circ }+z^{\circ }={180}^{\circ }$ ---(i)

It is given that, $\frac{y}{x}=5$

$\Rightarrow y=5x$ ---(ii)

and, $\frac{z}{x}=4$

$\Rightarrow z=4x$ ---(iii)

Substituting (ii) and (iii) in (i), we get:

$x^{\circ }+y^{\circ }+z^{\circ }={180}^{\circ }$

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

$\Rightarrow 10x^{\circ }={180}^{\circ }$

$\Rightarrow x^{\circ }=\frac{{180}^{\circ }}{10}$

$\Rightarrow x^{\circ }={18}^{\circ }$

Hence, the correct choice is (b).