Question 630711
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