Find the number of sides of a regular polygon, if each of its interior

1.	Find the number of sides of a regular polygon, if each of its interior angles is 3πc/4
Answer» Each interior angle of a regular polygon = \(\frac {3\pi}{4}\)= (\(\frac{3\pi}{4}\)x\(=\frac{180}{\pi}\))°= 135° Interior angle + Exterior angle = 180° ∴ Exterior angle = 180° – 135° = 45° Let the number of sides of the regular polygon be n. But in a regular polygon, exterior angle = 360^∘/no. of sides ∴ 45^∘= 360^∘/n ∴ n = 360^∘/45^∘=8 ∴ Number of sides of a regular polygon = 8.

Find the number of sides of a regular polygon, if each of its interior angles is 3πc/4

Answer»

Each interior angle of a regular polygon

= \(\frac {3\pi}{4}\)= (\(\frac{3\pi}{4}\)x\(=\frac{180}{\pi}\))°= 135°

Interior angle + Exterior angle = 180°

∴ Exterior angle = 180° – 135° = 45°

Let the number of sides of the regular polygon be n.

But in a regular polygon, exterior angle = 360^∘/no. of sides

∴ 45^∘= 360^∘/n

∴ n = 360^∘/45^∘=8

∴ Number of sides of a regular polygon = 8.