Question

In Fig. 91, AOB is a straight line and 4x = 5y. The value of x is
(a) 100
(b) 105
(c) 110
(d) 115

Answer 1

∠AOC + ∠BOC = 180^∘ [∵ Linear pair angles]
⇒ y^∘ + x^∘ = 180^∘
⇒ y + x = 180
$$\begin{gathered} \Rightarrow \frac{4x}{5}+x=180\left[\because 4x=5y\Rightarrow y=\frac{4x}{5}\right] \\ \Rightarrow 4x+5x=180\times 5 \\ \Rightarrow 9x=180\times 5 \\ \Rightarrow x=100 \end{gathered}$$
Hence, the correct answer is option (a).