If an interior angle of a regular polygon measures 144 how many sides does it have?

Question

Angles of polygons

Answer 1

Let S=number of sides. The angles at the centre are each 360/S these being the vertex angles of S triangles making up the polygon. The triangles are isosceles, so the other angles are (180-360/S)/2=90-180/S. Two of these angles in adjacent triangles form the interior angle of the polygon, so 180-360/S=144. So 36=360/S and S=360/36=10. The polygon has ten sides.