A) \[80{}^\circ ,\]\[60{}^\circ ,\]\[40{}^\circ \]
B) \[70{}^\circ ,\]\[50{}^\circ ,\]\[60{}^\circ \]
C) \[80,\]\[65{}^\circ ,\]\[35{}^\circ \]
D) \[80{}^\circ ,\]\[55{}^\circ ,\]\[45{}^\circ \]
Correct Answer: C
Solution :
| [c] Let \[\angle C=x\] Then, \[\angle B=30{}^\circ +\angle C=30{}^\circ +x\] and \[\angle A=15{}^\circ +\angle B=45{}^\circ +x\] Now, \[\angle A+B+\angle C=180{}^\circ \] \[\Rightarrow \] \[45{}^\circ +x+30{}^\circ +x+x=180{}^\circ \] \[\Rightarrow \] \[75{}^\circ +3x=180{}^\circ \]\[\Rightarrow \]\[3x=105{}^\circ \] \[\Rightarrow \] \[x=35{}^\circ \] \[\therefore \] \[\angle A=45{}^\circ +x{}^\circ =45{}^\circ +35{}^\circ =80{}^\circ \] \[\angle B=30{}^\circ +x{}^\circ =30{}^\circ +35{}^\circ =65{}^\circ \] \[\angle C=x{}^\circ =35{}^\circ \] |
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