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°

Answer 1

(a) 60°

Let
$\angle AOB=x°=\left(4a\right)°,\angle COB=y°=\left(5a\right)°\text{and}\angle BOD=z°=\left(6a\right)°$
Then, we have:
$$\begin{gathered} \angle AOB+\angle COB+\angle BOD=180°\left[\text{Since}\mathit{\text{AOB}}\text{is a straight line}\right] \\ \Rightarrow 4a+5a+6a=180° \\ \Rightarrow 15a=180° \\ \Rightarrow a=12° \\ \therefore y=5\times 12°=60° \end{gathered}$$