SOLUTION: one polygon has three more sides than another.how many more degrees are in the sum of the interior angle measures of the first polygon?

Question 630711: one polygon has three more sides than another.how many more degrees are in the sum
of the interior angle measures of the first polygon?
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
X = NUMBER OF SIDES OF ONE POLYGON
X+3 = NUMBER OF SIDES OF OTHER POLYGON
NUMBER OF DEGREES IN ONE POLYGON IS EQUAL TO 180 * (X-2)
NUMBER OF DEGREES IN OTHER POLYGON IS EQUAL TO 180 * (X-2+3)
DIFFERENCE IN DEGREES BETWEEN THE 2 IS:
180 * (X-2+3) MINUS (180 * (X-2))
SIMPLIFY THIS TO GET:
180 * (X+1) MINUS (180*(X-2))
SIMPLIFY FURTHER TO GET:
180*X + 180 MINUS (180*X - 360)
SIMPLIFY FURTHER TO GET:
180*X + 180 MINUS 180*X + 360
COMBINE LIKE TERMS TO GET:
+540
THE POLYGON WITH 3 MORE SIDES WILL HAVE 540 MORE DEGREES IN ITS SUM THAN THE POLYGON WITH 3 LESS SIDES.
AN EXAMPLE:
POLYGON WITH 3 SIDES IS EQUAL TO A SUM OF (3-2)*180 = 180
POLYGON WITH 6 SIDES IS EQUAL TO A SUM OF (6-2)*180 = 720
DIFFERENCE BETWEEN THE 2 IS 720 - 180 = 540

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
one polygon has three more sides than another.how many more degrees are in the sum
of the interior angle measures of the first polygon?
-------------
n sides --> 180*(n-2)
n+3 sides --> 180*(n+1)
-----------
difference = 540 degrees

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