SOLUTION: the sum of the interior angles in polygon E is 900 degrees more than the sum of interior angles in polygon F. The total number of the sides of the two polygons is 25. How many side

Algebra ->  Polygons -> SOLUTION: the sum of the interior angles in polygon E is 900 degrees more than the sum of interior angles in polygon F. The total number of the sides of the two polygons is 25. How many side      Log On


   

Question 1124004: the sum of the interior angles in polygon E is 900 degrees more than the sum of interior angles in polygon F. The total number of the sides of the two polygons is 25. How many sides in each polygon?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by ikleyn(52775) About Me  (Show Source):
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Let m and n are the numbers of sides of the two polygons.


Then your first equation is


((m-2)*180 - (n-2)*180 = 900,    or


(m-2) - (n-2) = 900/180 = 5,   or


m - n = 5.       (1)


Your second equation is


m + n = 25.      (2)


Add equations (1) and (2).


You get  2m = 5+25 = 30  ====>  m = 15.


Then from (2)  n = 25-15 = 10.


Answer.  15 and 10 sides.