SOLUTION: The sum of the interior angles of a polygon is twice the sum of its exterior angles. How many sides does the polygon have ?

Algebra.Com
Question 1122221: The sum of the interior angles of a polygon is twice the sum of its exterior angles. How many sides does the polygon have ?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the polygon has 6 sides.

the sum of the exterior angles of a polygon is always 360 degrees.

the sum of the interior angles of a polygon is equal to 180 * (n - 2).

n is equal to the number of sides of the polygon.

if the sum of the interior angles is twice the sum of the exterior angles, then the sum of the interior angles has to be 720 degrees.

720 = 180 * (n - 2)
divide both sides of this equation by 180 to get 720/180 = n - 2
simplify to get 4 = n - 2
solve for n to get n = 6


Answer by ikleyn(52775)   (Show Source): You can put this solution on YOUR website!
.
It is possible if and only if each interior angle is twice its exterior angle.


Since these angles are supplementary, it is possible only if all interior angles are 120 degrees each.


Hence, the polygon has 6 sides (hexagon).


RELATED QUESTIONS

IF the sum of the measures of the interior angles of a polygon is twice the sum of its... (answered by Gogonati)
If the sum of the measures of the interior angles of a polygon is twice the sum of its... (answered by jim_thompson5910)
The sum of interior angles of a convex polygon is ten times the sum of its exterior... (answered by reviewermath)
The sum of the interior angles of a polygon is twice the sum of its exterior angles. How... (answered by rothauserc)
How many sides has a polygon in which the sum of the interior angles of the polygon is... (answered by Alan3354)
How many sides does a polygon have if the sum of its interior angles is 7 times the sum... (answered by Theo,greenestamps)
How many sides does a polygon have if the sum of its interior angles is seven times the... (answered by Theo,greenestamps)
the sum of the measures of the interior angles of a polygon is the same as the sum of the (answered by Don2xmalabag)
The sum of the measures of the interior angles of a polygon Is five times the sum of the... (answered by stanbon)