The sum of the exterior angles of a polygon is 360o. Dividing 360o by the size of the exterior angle gives the number of sides.
If the interior angle is 144o, the exterior angle is 180o - 144o = 36o.
Number of sides = 360o / 36o = 10 (a decagon).
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If it is a regular polygon then it will have 10 sides
It will have 10 sides and it is a decagon
It is a decagon (10 sides) because if the interior angle is 144° then the exterior is 36°. 360 Divided by 36 is 10 and so it is a decagon.
interior angle = (sides - 2) * 180 / sides sides * interior angle = 180 * sides - 360 sides * (interior angle - 180) = -360 sides = -360 / (interior angle - 180) sides = 360 / (180 - interior angle) So, for 144 degrees: sides = 360 / 36 = 10
A regular polygon with interior angles of 144 degrees has 10 sides. Using the fact that a regular n-gon has interior angles of degree (n-2)*180/n, you can solve for the number of sides fairly easily.