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)
On adding
2A = 176\textdegree
=> A = \frac{176}{2} = 88\textdegree
From equation (1),
\therefore 88\textdegree+B = 140\textdegree
=> B = 140\textdegree - 88\textdegree = 52\textdegree
Hence option [D] is the right answer.

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