Question

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

• A. ${48}^o$
• B. ${38}^o$
• C. ${18}^o$
• D. ${46}^o$

Answer 1

Answer: (A)

${48}^o$

$a=4b$ 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
$\Rightarrow c=\frac{({21}^o+{75}^o)}{2}=\frac{{96}^o}{2}={48}^o$

Hence, option A is correct.