SOLUTION: If the number of sides of an n-sided regular polygon is increased by 4, each
interior angle is increased by 32°. How many sides are in the newly formed
regular polygon?
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Question 258750: If the number of sides of an n-sided regular polygon is increased by 4, each
interior angle is increased by 32°. How many sides are in the newly formed
regular polygon?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
If the number of sides of an n-sided regular polygon is increased by 4, each
interior angle is increased by 32°. How many sides are in the newly formed
----------------
Use the exterior angles, it's simpler.
Each exterior angle is decreased by 32 degs.
ext angle = 360/n
360/(n+4) = (360/n) - 32 = (360 - 32n)/n
cross multiply
360n = (n+4)*(360-32n) = -32n^2 + 232n + 1440
90n = -8n^2 + 58n + 360
8n^2 + 32n - 360 = 0
----------------------
n = -9 ignore
n = 5
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The original polygon has 5 sides. Increasing to 9 sides adds 32 degs to each interior angle.
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