In the adjoining figure, AOB is a straight line. If x : y : z = 4 : 5 : 6, then y = ?
Question:

In the adjoining figure, AOB is a straight line. If x : y : z = 4 : 5 : 6, then y = ?
(a) 60°
(b) 80°
(c) 48°
(d) 72°

 

Solution:

(a) 60°

Let  

$\angle A O B=x^{\circ}=(4 a)^{\circ}, \angle C O B=y^{\circ}=(5 a)^{\circ}$ and $\angle B O D=z^{\circ}=(6 a)^{\circ}$

Then, we have:

$\angle A O B+\angle C O B+\angle B O D=180^{\circ} \quad$ [Since $A O B$ is a straight line]

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

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

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

 

$\therefore y=5 \times 12^{\circ}=60^{\circ}$

 

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