In the adjoining figure, y = ?

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 $]$

$\Rightarrow 36^{\circ}+90^{\circ}+y=180^{\circ}$

$\Rightarrow y=54^{\circ}$

 

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