The interior angle of a regular polygon is 6 times its exterior angle find the…

Explanation

each interior angle of a polygon = \(\frac{(n - 2)\times 180}{n}\) where n = no of side of a polygon

each exterior angle of a polygon = \(\frac{360}{n}\)

then  \(\frac{(n - 2)\times 180}{n}\) = 6\(\times\) \(\frac{360}{n}\)

= (n - 2) 180 = 2160

= 180n - 360 = 2160

= 180n = 2160 + 360

= 180n = 2520

therefore, n = \(\frac{2520}{180}\) = 14.