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

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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.

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