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Question
AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = 20° ; find :
(i) its each interior angle,
(ii) its each exterior angle
(iii) the number of sides in the polygon.
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Solution
∵ Polygon is regular (Given)
∴ AB = BC
⇒ ∠BAC = ∠BCA ...[∠S opposite to equal sides]
But ∠BAC = 20°
∴ ∠BCA = 20°
i.e. In Δ ABC,
∠B + ∠BAC + ∠BCA = 180°
∠B + 20° + 20° = 180°
∠B = 180° - 40°
∠B = 140°
(i) each interior angle = 140°
(ii) each exterior angle = 180°- 140°= 40°
(iii) Let no. of. sides = n
`therefore 360^circ/"n" = 40^circ`
n = `360^circ/40^circ = 9`
n = 9
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