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Question
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.
Solution
Let number of sides of regular polygon = n
AB & DC when produced meet at P such that
∠P = 90°
∵ Interior angles are equal.
∴ ∠ABC = ∠BCD
∴ 180° - ∠ABC = 180° - ∠BCD
∴ ∠PBC = ∠BCP
But ∠P = 90° (given)
∴ ∠PBC + ∠BCP = 180° - 90° = 90°
∴ ∠PBC =∠BCP
`= 1/2 XX 90° = 45°`
∴ Each exterior angle = 45°
`therefore 45^circ = 360^circ/"n"`
n = `360^circ/45^circ`
n = 8
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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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