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A-regular-polygon-of-2k-1-sides-has-140-as-the-size-of-each-interior-angle-Find-k-




Question Number 58567 by olalekan2 last updated on 25/Apr/19
 A regular polygon of (2k+1) sides  has 140 as the size of each interior  angle.Find k
$$\:{A}\:{regular}\:{polygon}\:{of}\:\left(\mathrm{2}{k}+\mathrm{1}\right)\:{sides} \\ $$$${has}\:\mathrm{140}\:{as}\:{the}\:{size}\:{of}\:{each}\:{interior} \\ $$$${angle}.{Find}\:{k} \\ $$
Commented by mr W last updated on 25/Apr/19
(2k+1)(180−140)=360  2k+1=9  k=4
$$\left(\mathrm{2}{k}+\mathrm{1}\right)\left(\mathrm{180}−\mathrm{140}\right)=\mathrm{360} \\ $$$$\mathrm{2}{k}+\mathrm{1}=\mathrm{9} \\ $$$${k}=\mathrm{4} \\ $$

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