SOLUTION: Can someone help me with this question? The sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each

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Question 1096797: Can someone help me with this question?
The sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex. How many sides does the polygon have?
Thank you!
Found 2 solutions by MathTherapy, Alan3354:
Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Can someone help me with this question?
The sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex. How many sides does the polygon have?
Thank you!
The sum of the exterior angles of ANY polygon is 360%5Eo

Since the sum of the INTERIOR angles is 5 times the sum of the EXTERIOR angles, then the sum of the INTERIOR angles is: 5(360) = 1,800o

Formula for sum of interior angles (S) of a polygon: S = 180(n - 2), with n being the number of sides

1,800 = 180(n - 2)

180(10) = 180(n - 2)

10 = n - 2

n, or number of sides = highlight_green%28matrix%281%2C3%2C+10+%2B+2%2C+%22=%22%2C+12%29%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex. How many sides does the polygon have?
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Hint: The sum of exterior angles = 360 for all convex polygons.