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The difference between any two consecutive …

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The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°. Find the number of the sides of a polygon?
  • 1 answers

Vinay Yadav 5 years, 5 months ago

Sum of n side of polygon =(n-2)×180 Sn=180n-360 n/2(2a+(n-1)d)=180n-360 n/2(240+5n-5)=180n-360 n/2(235+5n)=180n-360 235n+5n**2=360n-720 5n**2-125+720=0 Dividing by 5 for simplify the equation Then we have n**2-25n+144=0 n**2-9n-16n+144=0 n(n-9)-16(n-9)=0 n-16=0. (n-9)=0 n=16. n=9 We take n=9 Because when n=16 180°<n ** Means power
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