Mathematics

# In the given figure, $PQ$ and $RS$ intersect each other at $O$. If $\angle ROT={75}^{o}$, find the value of $c$.

${48}^{o}$

##### SOLUTION
$a=4b$ and $2c=b+{75}^{o}$ (vert. opp $\angle s$)
Also $a+2c={180}^{o}$ ($PQ$ is a straight line)
$\Rightarrow$ $4b+b+{75}^{o}={180}^{o}$
$\Rightarrow$ $5b={105}^{o}$ $\Rightarrow$ $b={21}^{o}$
$\therefore a=4\times {21}^{o}={84}^{o}$ and
$\Rightarrow c=\cfrac{({21}^{o}+{75}^{o})}{2}=\cfrac{{96}^{o}}{2}={48}^{o}$
Hence, option A is correct.

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Single Correct Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
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