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

Question

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

Santosh Kumar · Accepted Answer

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°

$\Rightarrow ∠ AOB = \frac{90 °}{2}$

⇒ ∠AOB = 45°

Now,

∠AOB + ∠EOB = 180° (Angle on a straight line)

⇒ ∠EOB = 180° – 45°

⇒ ∠EOB = 135°

Interior angle of polygon $= \frac{(n - 2) \times 180 °}{n}$

Where, n = no.of sides in the polygon.

$\Rightarrow 135 ° = \frac{(n - 2) \times 180 °}{n} \Rightarrow 135 n = (n - 2) 180 \Rightarrow \frac{n}{n - 2} = \frac{4}{3} \Rightarrow 4 n - 8 = 3 n \Rightarrow n = 8$

∴ No. of sides in the polygon is 8.

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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