SOLUTION: Find the number of sides of a convex regular polygon who sum of the interior angles is 3 times the sum of the exterior angles.

Question 1171727: Find the number of sides of a convex regular polygon who sum of the interior angles is 3 times the sum of the exterior angles.
Answer by ikleyn(52782) (Show Source): You can put this solution on YOUR website!
.


Let n be the number of sides.


The sum of all exterior angles is 360  degrees.


From the condition, the sum of all interior angles is 3*360 = 1080 degrees.


It gives you an equation


    180*(n-2) = 1080


which implies


    n - 2 = 1080/180 = 6.


Hence,  n = 6 + 2 = 8.


ANSWER.  n = 8  (octagon).

Solved.

/\/\/\/\/\/\/

Notice that the assumption that the polygon is regular, is EXCESSIVE and UNNECESSARY:
I did not use it my solution.

The statement and the solution BOTH are valid for any convex polygon.

RELATED QUESTIONS
The sum of interior angles of a convex polygon is ten times the sum of its exterior... (answered by reviewermath)

Given that the sum of the interior angles of a regular polygon is four times the (answered by psbhowmick)

find the number of sides of a convex polygon whose sum of the measures of its interior... (answered by psbhowmick)

What is the sum of the exterior angles of a convex polygon with 100 sides... (answered by Alan3354,KMST)

The sum of interior angles of a regular polygon is 24 times the size of the exterior... (answered by ikleyn)

Find the measure of the sum of the exterior angles of a regular polygon with 20 sides?... (answered by stanbon)

the sum of the interior angles of a polygon is three times the sum of its exterior angles (answered by ikleyn)

a convex polygon has 20 sides, find the sum of the interior... (answered by jim_thompson5910)

a regular polygon has n sides. The sum of the interior angles of the polygon is 1260... (answered by Earlsdon)