Question:
In the adjoining figure, y = ?
(a) 36°
(b) 54°
(c) 63°
(d) 72°
Solution:
(b) 54°
We have:
$3 x+72=180^{\circ} \quad[\because A O B$ is a straight line $]$
$\Rightarrow 3 x=108$
$\Rightarrow x=36$
Also,
$\angle A O C+\angle C O D+\angle B O D=180^{\circ} \quad[\because A O B$ is a straight line $]$
$\Rightarrow 36^{\circ}+90^{\circ}+y=180^{\circ}$
$\Rightarrow y=54^{\circ}$