SOLUTION: #1 Question from the book: A polygon has n sides. Four of its exterior angles are 12, 25, 32 and 41 and the remaining (n - 4) exterior angles are each equal to 50. Find n. #2 Q

Question 91851: #1 Question from the book:
A polygon has n sides. Four of its exterior angles are 12, 25, 32 and 41 and the remaining (n - 4) exterior angles are each equal to 50. Find n.
#2 Question on pentagon:
If the angles of a pentagon are x, 1.5x, 2.5x, 3x and (2x - 20), find the value of x.

Answer by mathispowerful(115) (Show Source):
You can put this solution on YOUR website!
#1)The sum of exterior angles of a polygon can be represented by 180n + 360
where n is the number of sides in polygon.
in your case we need to add all angles together and let it equal to 180n+360,
so 12+25+32+41+50(n-4)= 180n + 360
110 + 50n - 200 = 180n + 360
simplify it: 130n = -450
n will be a negative number.
conclusion, this polygon doesn't exist! (double check your numbers in the question.
ACTUALLY, IT IS IMPOSSIBLE TO HAVE ALL EXTERIOR ANGLES SMALLER THAN 180 DEGREES
THIS IS A BAD OR ILL QUESTION.
Now let's try #2
The sum of interior angles of a pentagon is 540
x + 1.5x + 2.5x +3x + (2x - 20)= 540
simplify it: 10x - 20 = 540
10x = 560
x = 56