Question

the exterior angle of a regular polygon is one third the size of its interior angle. how many sides does the polygon have

Answer 1

8 sides

Explanation:

let x be the exterior angle then 3x is the interior angle

interior angle + exterior angle = 180° , then

x + 3x = 180

4x = 180 ( divide both sides by 4 )

x = 45

the sum of the exterior angles of a polygon = 360°

since the polygon is regular with each exterior angle = 45°, then

number of sides = 360° ÷ 45° = 8