How many sides does a regular polygon have if the outer angle is 5 times less than the inner one?

The sum of the outer and inner angles is 180˚ (they are adjacent). Let’s denote the outer corner by x˚, then the inner one is 5x˚. We get the equation:

x + 5x = 180;

6x = 180;

x = 30.

Thus, the external angle is 30˚, and the sum of all external angles, taken one at each vertex, is 360˚.

n = 360˚ / 30˚ = 12.

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