Two alternate sides of a regular polygon when produced meet at the right angle.Calculate the number of sides in the polygon.Please anwers required by experts only immediately
In a regular polygon, if two sides are extended and they meet at an angle of 90°, then both extended sides are equal.
OA = AB
∴ ∠AOB = ∠ABO
In ΔAOB,
∠AOB + ∠OAB + ∠ABO = 180°
⇒ 2∠AOB + ∠OAB = 180° (∠AOB = ∠ABO)
⇒ 2∠AOB = 180° – 90°
⇒ ∠AOB = 45°
Now,
∠AOB + ∠EOB = 180° (Angle on a straight line)
⇒ ∠EOB = 180° – 45°
⇒ ∠EOB = 135°
Interior angle of polygon
Where, n = no.of sides in the polygon.
∴ No. of sides in the polygon is 8.