Mathematics

Mark the correct alternative of the following.
In figure, if AOB and COD are straight lines. Then, $$x+y=?$$


ANSWER

$$140$$


SOLUTION

In figure, $$\angle AOC = \angle BOD$$                 (VOA)
$$\angle AOC = 3x^o$$   
$$\angle AOD = y^o$$                 (VOA)
$$y^o = (7x - 20)^o$$
$$\angle AOC + \angle COB + \angle BOD + \angle AOD = 360^o$$  
$$3x + (7x - 20) + 3x + (7x - 20) = 360^o$$  
$$3x + 7x - 20 + 3x + 7x - 20 = 360^o$$  
$$20x - 40 = 360^o$$  
$$20x = 360^o + 40$$  
$$20x = 400^o $$  
$$x = 20^o $$  
So, $$\angle BOD = 3x^o = 3 \times 20^o  = 60^o$$ 
$$\angle BOC = y^o = 7x - 30 = 7 \times 20^o  - 20= 120^o$$ 
$$x + y = 20 + 120 = 140^o$$

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Single Correct Medium Published on 09th 09, 2020
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