Question 946797

{{{Sum_ of_ Interior_ Angles_ of_ a_ Polygon= 180(n - 2)}}} where {{{n}}} = number of sides 

so, the sum of the interior angles of a 
(a) square is 

{{{n=4}}}
{{{Sum_ of_ Interior_ Angles_ of_ a_ square= 180(4 - 2)}}}

{{{Sum_ of_ Interior_ Angles_ of_ a_ square= 180(2)}}}

{{{Sum_ of_ Interior_ Angles_ of_ a_ square= 360}}}

(b) pentagon

{{{n=5}}}
 {{{Sum_ of_ Interior_ Angles_ of_ a_ pentagon= 180(5 - 2)}}}

{{{Sum_ of_ Interior_ Angles_ of_ a_ pentagon= 180(3)}}}

{{{Sum_ of_ Interior_ Angles_ of_ a_ pentagon= 540}}}



(c) hexagon 
{{{n=6}}}



 {{{Sum_ of_ Interior_ Angles_ of_ a_ hexagon= 180(6 - 2)}}}

 {{{Sum_ of_ Interior_ Angles_ of_ a_ hexagon= 180(4)}}}

 {{{Sum_ of_ Interior_ Angles_ of_ a_ hexagon= 720}}}


(d) octagon

{{{n=8}}}

  {{{Sum_ of_ Interior_ Angles_ of_ a_ octagon= 180(8 - 2)}}}

 {{{Sum_ of_ Interior_ Angles_ of_ a_ octagon= 180(6)}}}

 {{{Sum_ of_ Interior_ Angles_ of_ a_ octagon= 1080}}}


(e) decagon,

{{{n=10}}}
  {{{Sum_ of_ Interior_ Angles_ of_ a_ decagon= 180(10 - 2)}}}
 {{{Sum_ of_ Interior_ Angles_ of_ a_ decagon= 180(8)}}}
 {{{Sum_ of_ Interior_ Angles_ of_ a_ decagon= 1440}}}


(f) 100-gon,

 {{{n=100}}}

{{{Sum_ of_ Interior_ Angles_ of_ a_ 100-gon= 180(100 - 2)}}}
 {{{Sum_ of_ Interior_ Angles_ of_ a_ 100-gon= 180(98)}}}
 {{{Sum_ of_ Interior_ Angles_ of_ a_ 100-gon= 17640}}}

(g) 1000-gon

{{{n=1000}}}

{{{Sum_ of_ Interior_ Angles_ of_ a_ 1000-gon= 180(1000 - 2)}}}
 {{{Sum_ of_ Interior_ Angles_ of_ a_ 1000-gon= 180(998)}}}
 {{{Sum_ of_ Interior_ Angles_ of_ a_ 1000-gon= 179640}}}