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If the two consecutive interior angles of a polygon differ by 5 degrees and the shortest angle is 120 deg.Then detemine the sides of the polygon.

If the two consecutive interior angles of a polygon differ by 5 degrees and the shortest angle is 120 deg.Then detemine the sides of the polygon.

Grade:12

1 Answers

Sukhendra Reddy Rompally B.Tech Mining Machinery Engg, ISM Dhanbad
93 Points
11 years ago
Dear student, the sum of all interior angles for an n-sided polygon=(n-2)180°.you can check it by substuting different values of n.now,the sum of all interior angles of the given polygon is an A.P with first term 120° and common difference 5° ,which is given by n/2 (2*120° + (n-1)5°) = n/2 (235 - 5n) = 180(n-2). Solve the quadratic to get = 9 or n = 16. Hope you understand the solution.if not,feel free to call me on 07209736303. ALL THE BEST. PLZZ APPROVE MY ANSWER IF YOU LIKE IT

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