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

$144^o$

##### 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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