Mathematics

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


ANSWER

$${48}^{o}$$


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
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