If the ratio of an external angle and an internal angle of a regular polygon is 1 : 5, then what is the number of sides in the polygon?
Answer & explanation
Correct answer: option 3
We have,
The ratio between exterior angle and interior angle of a regular polygon = 1 : 5.
Let the interior angle be 5a and the exterior angle be a.
We know that,
Exterior angle = 180° - interior angle.
a = 180° - 5a
Now, a + 5a = 180°
6a = 180°
a = 30°
Exterior angle = 30°.
The number of sides of a polygon = 360°/measure of exterior angle
= 360°/30° = 12