A) \[120{}^\circ ,\text{ }40{}^\circ ,\text{ }20{}^\circ \]
B) \[120{}^\circ ,\text{ }30{}^\circ ,\text{ }30{}^\circ \]
C) \[90{}^\circ ,\text{ }45{}^\circ ,\text{ }45{}^\circ \]
D) \[~90{}^\circ ,\text{ }60{}^\circ ,\text{ }30{}^\circ \]
Correct Answer: B
Solution :
Let the angles be \[x,\,\,y,\,\,z\] (\[x\] is largest and \[z\] is smallest) Then\[,\] \[x+y+z={{180}^{o}}\] ? (i) \[x=2(y+z)\] or \[2x=4y+4z\] ? (ii) and \[z=\frac{x}{4}\] or \[x=4z\] ? (iii) From equations (ii) and (iii), we get \[x=4y\] ? (iv) From equations (iii) and (iv), we get \[y=z\] ? (v) From equations (i), (iii) and (iv), we get \[4z+z+z={{180}^{o}}\] or \[z={{30}^{o}}\] Hence angles are\[{{120}^{o}},\,\,{{30}^{o}},\,\,{{30}^{o}}\]
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