Question

In the adjoining figure, y = ?
(a) 36°
(b) 54°
(c) 63°
(d) 72°

Answer 1

(b) 54°

We have:
$$\begin{gathered} 3x+72=180°\left[\because AOB\text{is a straight line}\right] \\ \Rightarrow 3x=108 \\ \Rightarrow x=36 \end{gathered}$$
Also,
$$\begin{gathered} \angle AOC+\angle COD+\angle BOD=180°\left[\because AOB\text{is a straight line}\right] \\ \Rightarrow 36°+90°+y=180° \\ \Rightarrow y=54° \end{gathered}$$