| In \[\Delta ABC,\]\[\angle A=30{}^\circ ,\]\[\angle B=60{}^\circ .\] Find \[\angle C\] in circular measure. [SSC (10+2) 2012] |
A) \[\frac{2{{\pi }^{c}}}{3}\]
B) \[\frac{3{{\pi }^{c}}}{4}\]
C) \[\frac{{{\pi }^{c}}}{6}\]
D) \[\frac{{{\pi }^{c}}}{2}\]
Correct Answer: D
Solution :
| In \[\Delta ABC,\] |
| \[\angle A+\angle B+\angle C=180{}^\circ \][by angle sum property] |
| \[\angle C=180{}^\circ -(30{}^\circ +60{}^\circ )=90{}^\circ \] |
| \[\because \] \[180{}^\circ =\pi \,\,\text{radian}\] |
| \[\therefore \] \[90{}^\circ =\frac{\pi }{180{}^\circ }\times 90{}^\circ \] |
| \[\therefore \] \[\angle C=\frac{\pi }{2}\,\,\text{radian}\] |
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