Mathematics

# Of the three angles of a triangle, one is half of the greatest and thrice the smallest then find the angles

##### SOLUTION
$\begin{array}{l} Let\, the\, angle\, be\, x \\ greatest\, \, angle=2x \\ smallest\, angle=\dfrac { x }{ 3 } \\ Now \\ x+2x+\dfrac { x }{ 3 } =180 \\ \Rightarrow 10x=180\times 3 \\ \Rightarrow 10x=540 \\ \therefore x=54 \\ Then \\ greatest\, \, angle=2\times 54=108 \\ smallest\, angle=\dfrac { { 54 } }{ 3 } =18 \end{array}$

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