In the adjoining figure, x:y:z = 5:4:6. If XOY is a straight line,


In the adjoining figure, x:y:z = 5:4:6. If XOY is a straight line, find the values of xy and z.


Let $x=5 a, y=4 a$ and $z=6 a$

XOY is a straight line. Therefore,

$\angle X O P+\angle P O Q+\angle Y O Q=180^{\circ}$

$\Rightarrow 5 a+4 a+6 a=180^{\circ}$

$\Rightarrow 15 a=180^{\circ}$

$\Rightarrow a=12^{\circ}$


$x \Rightarrow 5 \times 12^{\circ}=60^{\circ}$

$y \Rightarrow 4 \times 12^{\circ}=48^{\circ}$

and $z \Rightarrow 6 \times 12^{\circ}=72^{\circ}$


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