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प्रश्न
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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उत्तर
∵ 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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संबंधित प्रश्न
Fill in the blanks :
In case of regular polygon, with :
| No.of.sides | Each exterior angle | Each interior angle |
| (i) ___8___ | _______ | ______ |
| (ii) ___12____ | _______ | ______ |
| (iii) _________ | _____72°_____ | ______ |
| (iv) _________ | _____45°_____ | ______ |
| (v) _________ | __________ | _____150°_____ |
| (vi) ________ | __________ | ______140°____ |
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Is it possible to have a regular polygon whose interior angle is: 135°
Which formula correctly represents the sum of interior angles of an n-sided polygon?
