Question

5) The sum of interior angles of a regular polygon is equal to six times
the sum of exterior angles. Find the number of sides of the polygon.​

Answer 1

Answer:

The answer is 6 sides. First the problem is not written well. It should say the sum of the interior angles of a regular polygon is twice the sum of its exterior angles one at each vertex. The polygon is a hexagon. Each interior angle is 120 degrees. Each exterior is 60 degrees. The sum of the exterior angles one at each vertex is 460 degrees. The sum of the interior angles would be 6X120 or 720. 720 is twuce 360 If you have a triangle that is equilateral, each interior angle is 60 each exterior is 120. The sum of the exterior angles 360. If you have a square the interior angles are all 90, the exterior angles are also 90 and the sum of the exterior angles is again 360, Remember to find the exterior angles you extend one side of the polygon so the angle formed is between the extended side and the side of the triangle it is closest to.