Question

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

Answer 1

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