Each exterior angle of a regular polygon is 100 degree C less than the interior angle, calculate the size of the exterior angle

Question

parallel lines

Answer 1

The exterior angle=360/n where n is the number of sides.

The polygon can be split into isosceles triangles created by joining the centre to each vertex. So n triangles are created. The vertex angle (at the centre) is also 360/n. The other two angles of the triangle add up to 180-360/n=180(n-2)/n, and this is also the measure of the interior angle of the polygon, so 180(n-2)/n-360/n=100, from which we get 180n-360-360=100n. Therefore 80n=720 and n=9. In figures, the exterior angle is 40 and the interior angle is 140.