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Grade 11Algebra

Determine the number of sides of the convex polygon if largest interior angle is 172 degree and common difference is 4 degree

Profile image of Gaurav
7 Years agoGrade 11
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1 Answer

Profile image of Arun
7 Years ago
he exterior angles also must form an arithmetic progression, with 8° the least angle, and common difference 4°. 

Let n be the number of sides. The some of the n exterior angles is 360°. 

nth exterior angle = (n + 1)4° 

(n/2)[2(8°) + (n - 1)(4°)] = 360° 
(n/2)[2(8) + (n - 1)(4)] = 360 
(n/2)(4n + 12) = 360 
2n² + 6n - 360 = 0 
n² + 3n - 180 = 0 
(n + 15)(n - 12) = 0 

Reject the negative solution. 

n = 12 

The polygon has twelve side

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