Question

KL, LM and MN are three consecutive sides of a regular polygon. If ∠LKM = 20°, find the interior angle of the polygon and the number of sides of the polygon.

Answer 1

In ΔLMK, LM = LK            ...[Sides of a regular polygon]
∴ ∠LMK = ∠LKM = 20°  ...[Angles opp to equal sides are equal]
∴ ∠LKM + ∠LMK + ∠KLM = 180°
⇒ 20° + 20° + ∠KLM = 180°
⇒ ∠KLM = 140°
∴ Each interior angle of the polygon is 140°.

∴ Each interior angle of a regular polygon

= `(("n" - 2) xx 180°)/"n"`

⇒ `(("n" - 2) xx 180°)/"n"` = 140°

⇒ 180°(n - 2) = 140°n
⇒  40°n = 360°
∴ n = 9
∴ Number of sides of the polygon = 9.