Question & Answer » Mathematics Questions » The Interior Angles of a Polygon are in A.P. The Smallest angle is 120° and the Common Difference is 5° then find the number of sides of the Polygon.
unacademy_centre

The Interior Angles of a Polygon are in A.P. The Smallest angle is 120° and the Common Difference is 5° then find the number of sides of the Polygon.

The interior angles of a polygon are in AP. The smallest angle is 120 degrees and the common difference is 5 degrees then find the number of sides of the polygon. Find the answer to this question and access a vast question bank that is customized for learners.

Table of Content

Answer:- Let number in the polygon be ‘n’. The total sum of a polygon’s interior angles can be (n-2) *180°.

According to the question– 

  1. Smallest angle is 120°
  2. Common difference is 5°

Sum polygon’s interior angle – 

n/2 [2*120 + (n-1) *5]

Therefore, 

n/2[2*120 + (n-1)5] = (n-2) *180

Thus, 

n/2[5n+235] = (n-2) *180

Thus, 

5n2 + 235n + 360n – 720

Thus, n2 – 25n + 144 = Zero

Thus,

(n-16) (n-9) = 0

 n = 16, 9

If n = 16 then 16th angle = 120 + 15*5 = 195 > 180°, this is impossible. 

Answer =9. 

combat_iitjee

Trending Questions

testseries_iitjee
Download JEE Main 2022 Question Papers
.