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.