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.
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.
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.
