what are the sizes of an interior and exterior angle in a regular polygon?

Question

my teacher told me that the exterior angles of all regular polygon are 160 degree and she then asked why. and i cant find out then asked me the sum of interior anglesfrom triangles to decagon ??  pleez help me!!

Answer 1

If the number of sides of the regular polygon is n, then the sum of the exterior angles is 360°. Therefore, each exterior angle is 360/n degrees. The interior angle plus exterior angle must add up to 180°. So the interior angle is 180-(360/n). The total of the interior angles is n(180-(360/n))=180n-360 or 180(n-2). If n=3 (triangle) the angles add up to 180°. If n=4 (square) the total is 360°, the same as the exterior. If n=6 (hexagon) the total is 720°. I hope this helps.