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Normally I have seen questions such as

Find the angles of Triangle with Ratios 2:3:7. The best method to solve this would be to solve for x using the equation 2x+3x+7x=180

Recently I have solved many questions involving ratios and I have seen that in case we know the overall sum of the ratios involved as above (Sum of angles of triangle is 180) we simply need to sum those ratios up so that they equal to a given value. What I don't understand is how has the above equation (2x+3x+7x = 180) has been constructed why did we simply add an x after each ratio ?

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If three quantities are in the ratio $2:3:7$ for example, it means that for every $2$ portions of the first, we have $3$ of the second and $7$ of the third. We don't know exactly what quantities these are but adding the $x$ there takes care of this. $x$ just represents one portion of the quantity, so that $2x$, $3x$ and $7x$ represent $2$, $3$ and $7$ portions respectively.

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Normally I would solve this by a method more familiar to me like for the smallest angle (2/12)(180) for the next angle (3/12)180. – Rajeshwar Jul 7 '12 at 23:50

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