Question

ab,bc and cd are the three consecutive of a regular polygon. If angle bac = 15 degree find each interior angle of the polygon

Answer 1

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.