SOLUTION: the sum of the interior angles of a polygon is three times the sum of its exterior angles . Determine the number of sides of the polygon
Algebra ->
Polygons
-> SOLUTION: the sum of the interior angles of a polygon is three times the sum of its exterior angles . Determine the number of sides of the polygon
Log On
Question 1040556: the sum of the interior angles of a polygon is three times the sum of its exterior angles . Determine the number of sides of the polygon Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
the sum of the interior angles of a polygon is three times the sum of its exterior angles . Determine the number of sides of the polygon
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(n-2)*180 = 3*360 ---> (Everybody knows about the left side. It is the sum of internal angles of any n-sided polygon.
Many know about the number 360 in the right side. 360° is the sum of the external angles of any n-sided polygon.)
n- 2 = = 3*2 = 6 --->
n = 6 + 2 = 8.
Check. (8-2)*180 = 6*180. 6*180 in the left = 3*360 in the right. Yes!!!
Answer. n = 8. ( Octagon ! )