Aptitude Question ID : 92990
If the sum and difference of two angles are $latex \frac{22}{9} radian&s=1$ and $latex 36\textdegree$ respectively, then the value of smaller angle in degree taking the value of $latex \pi$ as $latex \frac{22}{7}&s=1$ is :
[A]$latex 48\textdegree$
[B]$latex 60\textdegree$
[C]$latex 56\textdegree$
[D]$latex 52\textdegree$
$latex \mathbf{52\textdegree}$
$latex \because \pi radian = 180\textdegree&s=1$
$latex \therefore \frac{22}{9}radian = \frac{180}{\pi}\times\frac{22}{9}&s=1$
$latex = \frac{180}{22}\times \frac{22\times7}{9} = 140\textdegree&s=1$….(1)
According to the question,
$latex A + B = 140\textdegree$
and, $latex A – B = 36\textdegree$ ……(2)
On adding
$latex 2A = 176\textdegree$
$latex => A = \frac{176}{2} = 88\textdegree&s=1$
From equation (1),
$latex \therefore 88\textdegree+B = 140\textdegree$
$latex => B = 140\textdegree – 88\textdegree = 52\textdegree$
Hence option [D] is the right answer.