SOLUTION: The sum of the interior angles of a polygon of n sides is 900. find the value of n.

Question 1181122: The sum of the interior angles of a polygon of n sides is 900.
find the value of n.
Found 3 solutions by Theo, MathTherapy, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the sum of the interior angles formula is:
S = 180 * (n - 2)
for a triangle, the sum is 180 * 1 = 180 degrees.
for a quadrilateral, the sum is 180 * 2 = 360 degrees.
if the sum is 900 degrees, then the formula becomes:
900 = 180 * (n - 2)
simplify to get 900 = 180 * n - 360
add 360 to both sides to get 1260 = 180 * n
divide both sides by 180 to get n = 1260 / 180 = 7
the number of sides = 7.
since the sum of the interior angles = 900, then each interior angle = 900 / 7 = 128.5714286 degrees.

Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

The sum of the interior angles of a polygon of n sides is 900.
find the value of n.

It is TRUE that this polygon has 7 sides.
However, it is NOT TRUE - as the other person stated - that each interior angle is , since itw's never indicated that the polygon is REGULAR.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

You write the equation as you read the problem 900 = 180*(n-2) degrees (the sum of interior angles of an n-gon) You cancel the factor 180 in both sides 5 = n-2. From it, you find the ANSWER to your problem n = 5 + 2 = 7.

That is all.

No need to write multi-line solution for such simple problem.

RELATED QUESTIONS
the sum of interior angles of a polygon with (2n-3) sides is equal to 62 right angles... (answered by psbhowmick)
a regular polygon of n-sides is such that each interior angle is 120 degree greatet than... (answered by Boreal,ikleyn)
a regular polygon has n sides. The sum of the interior angles of the polygon is 1260... (answered by Earlsdon)
Starting from the sum of exterior angles prove that in a regular polygon of n sides, the... (answered by solver91311)
A polygon has n sides.If one of its interior angles is 84� and the other interior angles... (answered by Edwin McCravy)
A polygon of n sides has half of the interior angles as 150 degrees each and the rest 170 (answered by Alan3354,greenestamps)
the sum of a polygon with (2n-3)sides is 62 right angles. find the value of... (answered by ccs2011)
One of the interior angles of the polygon with n sides is 124 degrees and the other (n-1) (answered by srinivas.g)
A polygon has n sides twp of the exterior angles are 41 each and five of the interior... (answered by solver91311)