Question

AB,BC and CD are the three consecutive sides of a regular polygon. If 1) each interior < of polygon
2)each exterior < of the polygon
3) number of sides in the polygon

Answer 1

AB, BC and CD are the consecutive sides of a regular polygon.  ∠BAC = 20°, AB = BC ⇒ ∠BAC = ∠BCA ∴ ∠BCA = 20° ⇒ ∠ABC = 180° - (20° + 20°) = 140°. Each interior angle of a regular polygon = [(2n - 4) x 90°] / n where n is the number of sides of the polygon. ⇒ 140° = [(2n - 4) x 90°] / n ⇒ 140°n = 180° n - 360° ⇒ 40° n = 360° ⇒ n = 9 Therefore, number of sides of the polygon is 9. 2) Each exterior angle of a regular polygon = (360°) / n where n is the number of sides of the polygon. 360°/9 = 40° Hence, each exterior angle of the polygon is 40°. 3) Each interior angle of a regular polygon =  (2n - 4) / n × 90° .where n is the number of sides of the polygon. Here n = 9 ⇒ (18 - 4) / 9 × 90° = 14 × 10° = 140°