# Aptitude Question ID : 92982

In the sum of two angles is $135\textdegree$ and their difference is $\frac{\pi}{12}$. Then the circular measure of the greater angle is :
[A]$\frac{\pi}{3}$
[B]$\frac{5\pi}{12}$
[C]$\frac{2\pi}{3}$
[D]$\frac{3\pi}{5}$

$\mathbf{\frac{5\pi}{12}}$
Two angles = A and B where A > B.
$\therefore A + B = 135\textdegree$
$= \left ( \frac{135\times \pi}{180} \right ) radian$
$=> A + B = \left ( \frac{3\pi}{4} \right ) radian$…..(1)
$A - B = \frac{\pi}{12}$…..(2)
$2A = \frac{3\pi}{4} + \frac{\pi}{12}$
$= \frac{9\pi+\pi}{12} = \frac{10\pi}{12} = \frac{5\pi}{6}$
$\therefore A = \frac{5\pi}{12}radian$
Hence option [B] is the right answer.