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The interior angles of a rectilinear figure are in A.P.if the least angle is 42degrees and the common difference is 33degrees find the number of sides

The interior angles of a rectilinear figure are in A.P.if the least angle is 42degrees and the common difference is 33degrees find the number of sides

Grade:10

1 Answers

sriram
11 Points
6 years ago
In general, the sum of interior angles of a rectilinear figure with ‘n’ sides = (2n – 4) Right Angles 
                                                                                                                  = (2n – 4) * 90 = 180n – 360 ------ (1)
Given, a = 420; d = 330. 
Assume the number of edges = n.
Then Sum of ‘n’ terms of an AP: Sn = \frac{n}{2}({2a+(n-1)d})
From (1),
180n – 360 = \frac{n}{2}({2*42+(n-1)33})
360n – 720 = 84n + 33n2 – 33n 
33n2 + 51n – 360n + 720 = 0
33n2 – 309n + 720 = 0
Solving the quadractic equation, n = 4.36, 5
As ‘n’ can not be in decimal point, n = 5.
 

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