Sum

Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.

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#### 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

Concept: Regular Polynomial

Is there an error in this question or solution?

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