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