Question

In a polygon, there are 3 right angles and the remaining angles are equal to 165°. Find the number of sides in the polygon.

Answer 1

Let the number of sides of the polygon be n
Number of right angles = 3
∴ Number of angles of 165° each = n - 3
Sum of interior angles of a polygon = (n - 2) x 180
⇒ 3 x 90° + (n - 3)165° = 180°n - 360°
⇒ 270° + 165°n - 495° = 180°n - 360°
⇒ 180°n - 165°k = 270° - 495° + 360°
⇒ 15°n = 135°
⇒ n = 9
Thus, the number of sides in the polygon is 9.