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We know that,
Sum of an exterior angle and an interior angle of polygon = 180°
Now,
Ratio of the an exterior angle and an interior angle = 1 : 5
Let the exterior angle be x and interior angle be 5x.
Therefore,
x + 5x = 180°
6x = 180°
x = 180°/6
x = 30°
Now,
The exterior angle = x = 30°
The interior angle = 5x = 5 * 30° = 150°
Now,
We know that the number of sides in a regular polygon, n = 360°/Exterior Angle
n = 360°/30°
n = 36/3
n = 12
Hence,
The number of sides = 12
Sum of an exterior angle and an interior angle of polygon = 180°
Now,
Ratio of the an exterior angle and an interior angle = 1 : 5
Let the exterior angle be x and interior angle be 5x.
Therefore,
x + 5x = 180°
6x = 180°
x = 180°/6
x = 30°
Now,
The exterior angle = x = 30°
The interior angle = 5x = 5 * 30° = 150°
Now,
We know that the number of sides in a regular polygon, n = 360°/Exterior Angle
n = 360°/30°
n = 36/3
n = 12
Hence,
The number of sides = 12
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