# ratio of the internal angle and the external angle of a regular polygon 5:1.how many sides does it have ?

their ratio = 5:1

so, external angle = 1/(5+1) * 180 = 1/6 * 180 = 30

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number of sides = 360/external angle = 360/30 = 12

------or------

let internal angle angle external angle be 5x and x respectively

so, 5x + x = 180

or 6x = 180

or x = 180/6 = 30

so, external angle = 30

number of sides = 360/external angle = 360/30 = 12