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

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:

From (1),

180n – 360 = 

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.