A) \[\left[ \frac{180}{\pi }-1 \right]\]
B) \[\left[ 1-\frac{\pi }{180} \right]\]
C) \[\frac{1}{2}\left[ 1-\frac{\pi }{180} \right]\]
D) \[\frac{1}{2}\left[ \frac{180}{\pi }-1 \right]\]
Correct Answer: C
Solution :
Let the angles are \[\alpha \]and \[\beta ,\] then \[\alpha -\beta =1{}^\circ \] \[\Rightarrow \,\,\alpha -\beta =\frac{\pi }{180{}^\circ }\] is circular measure .. .(i) As given, \[\alpha +\beta =1\] ...(ii) On solving Eqs. (i) and (ii), we get, \[\alpha =\frac{1}{2}\left[ 1+\frac{\pi }{180{}^\circ } \right]\] and \[\beta =\frac{1}{2}\left[ 1-\frac{\pi }{180{}^\circ } \right]\] \[\beta \] is the smaller angle. Hence, smaller angle \[=\frac{1}{2}\left[ 1-\frac{\pi }{180{}^\circ } \right]\]
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