Aptitude Question ID : 92982
In the sum of two angles is $latex 135\textdegree$ and their difference is $latex \frac{\pi}{12}&s=1$. Then the circular measure of the greater angle is :
[A]$latex \frac{\pi}{3}&s=1$
[B]$latex \frac{5\pi}{12}&s=1$
[C]$latex \frac{2\pi}{3}&s=1$
[D]$latex \frac{3\pi}{5}&s=1$
$latex \mathbf{\frac{5\pi}{12}}&s=1$
Two angles = A and B where A > B.
$latex \therefore A + B = 135\textdegree$
$latex = \left ( \frac{135\times \pi}{180} \right ) radian&s=1$
$latex => A + B = \left ( \frac{3\pi}{4} \right ) radian&s=1$…..(1)
$latex A – B = \frac{\pi}{12}&s=1$…..(2)
On adding these equations,
$latex 2A = \frac{3\pi}{4} + \frac{\pi}{12}&s=1$
$latex = \frac{9\pi+\pi}{12} = \frac{10\pi}{12} = \frac{5\pi}{6}&s=1$
$latex \therefore A = \frac{5\pi}{12}radian&s=1$
Hence option [B] is the right answer.