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)
On adding these equations,
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.

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