Question

In Fig., OA and OB are opposite rays:


(i) If x = 25°, what is the value of y?
(ii) If y = 35°, what is the value of x?

Answer 1

$\angle$AOC + $\angle$BOC = 180° (Linear pair)
$$\begin{gathered} \Rightarrow \left(2y+5\right)+3x=180° \\ \Rightarrow 3x+2y=175° \end{gathered}$$
(i) If x = 25°, then
$$\begin{gathered} 3\times 25°+2y=175° \\ \Rightarrow 75°+2y=175° \\ \Rightarrow 2y=175°-75°=100° \\ \Rightarrow y=\frac{100°}{2}=50° \end{gathered}$$
(ii) If y = 35°, then
$$\begin{gathered} 3x+2\times 35°=175° \\ \Rightarrow 3x+70°=175° \\ \Rightarrow 3x=175°-70°=105° \\ \Rightarrow x=\frac{105°}{3}=35° \end{gathered}$$