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14 Jan 2019, 11:25
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D
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If all the internal angles of the convex polygon are distinct integers, what is the maximum number of sides the polygon can have?
I) The smallest exterior angle of the polygon is \(70^{\circ}\).
II) The average of all internal angles = \(108^{\circ}\).
I) The smallest exterior angle of the polygon is \(70^{\circ}\).
II) The average of all internal angles = \(108^{\circ}\).
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14 Jan 2019, 16:37
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zubair123
Statement 1: The smallest exterior angle of the polygon is \(70^{\circ}\).
it means that the largest interior angle is 110.
as all the interior angles are distinct integers, then the sum of angles would be at most (110+109+108+ ...)
so the sum of angles of a polygon with 'n' sides <110n,
As the formula of sum of interior angles of a polygon with n sides = (n – 2)*180,
then (n – 2)*180 < 110n
180n - 360 < 110n
n<5.14
so the maximum number of sides is 5
(sufficient)
Statement 2: The average of all internal angles = \(108^{\circ}\).
then the sum of all interior angles = 108n
and 108n = (n-2)*180
108n = 180n - 360
72n = 360
n = 5
(sufficient)
"D"
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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
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Thank you for understanding, and happy exploring!
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