Mathematics

In figure, lines $$PQ$$ and $$ST$$ intersect at $$O$$. If $$\angle POR=90^o$$ and $$x:y =3:2$$, then $$z$$ is equal to 


ANSWER

$$144^o$$


SOLUTION
We can see in the given figure, $$PQ$$ is a straight line 
$$\therefore \angle POR +ROT +\angle TOQ =180^o$$
$$\Rightarrow 90^o +x+y=180^o$$
$$\Rightarrow  x+y=90^o$$
$$\Rightarrow  x+y=90^o$$     ...(1)
Given that, $$\dfrac xy =\dfrac 32$$
Let $$x=3K$$ and $$y=2K$$
From equation (1) 
$$\Rightarrow 3K+2K=90^o$$
$$\Rightarrow  K=\dfrac{90^o}{5}$$
$$\Rightarrow  K=18^o$$
$$\therefore y=2\times 18^o =36^o$$
Now, $$SOT$$ is a straight line 
$$\Rightarrow z+y=180^o$$
$$\Rightarrow z+36^o =180^o$$
$$\Rightarrow z=180^o-36^o$$
$$\Rightarrow  z=144^o$$
Hence, Option $$(B)$$ is correct.

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Single Correct Medium Published on 09th 09, 2020
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