# Aptitude Question ID : 92990

If the sum and difference of two angles are $\frac{22}{9} radian$ and $36\textdegree$ respectively, then the value of smaller angle in degree taking the value of $\pi$ as $\frac{22}{7}$ is :
[A]$48\textdegree$
[B]$60\textdegree$
[C]$56\textdegree$
[D]$52\textdegree$

$\mathbf{52\textdegree}$
$\because \pi radian = 180\textdegree$
$\therefore \frac{22}{9}radian = \frac{180}{\pi}\times\frac{22}{9}$
$= \frac{180}{22}\times \frac{22\times7}{9} = 140\textdegree$….(1)
According to the question,
$A + B = 140\textdegree$
and, $A - B = 36\textdegree$ ……(2)
$2A = 176\textdegree$
$=> A = \frac{176}{2} = 88\textdegree$
$\therefore 88\textdegree+B = 140\textdegree$
$=> B = 140\textdegree - 88\textdegree = 52\textdegree$