# maths

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each interior angle of a regular polygon is 18 degree more than eight times an exterior angle. the number os sides of polygon is.

• maths -

at each vertex, interior + exterior = 180 degrees.

If exterior = x,

x+(8x+18) = 180
9x = 162
x = 18

he exterior angle of a regular n-gon is 360/n, so

18 = 360/n
n = 20

• maths -

Interior angle = 180 - (exterior angle) = 180 -360/N

Exterior angle = 360/N

180 - (360/N) = [8*360/N] +18
9*360/N = 162
N = 20 sides

It is called an icosagon

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