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# Regular polygon X has r sides, and each vertex has an angle measure of

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
Regular polygon X has r sides, and each vertex has an angle measure of  [#permalink]

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21 Jul 2017, 00:44
00:00

Difficulty:

65% (hard)

Question Stats:

35% (02:36) correct 65% (02:48) wrong based on 39 sessions

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Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of Polygon Q?

A. 2
B. 160
C. 176
D. 178
E. 179

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Re: Regular polygon X has r sides, and each vertex has an angle measure of  [#permalink]

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23 Jul 2017, 20:10
1
Bunuel wrote:
Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of Polygon Q?

A. 2
B. 160
C. 176
D. 178
E. 179

Total angle measure of a polygon = (n-2)*180
Interior angle of a regular polygon = (n-2)*180/n
The maximum value of interior angle has to be less than 180 and since it is specified to be a integer here . Let's equate it with 179 .
(n-2)*180 / n = 179
=> 180n - 360 = 179n
=> n = 360
Polygon X has 360 sides and each angle has a measure of 179 .

Now Polygon Q has 90 sides and angle measure = 88*180 / 90
=176

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Joined: 02 Mar 2017
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Regular polygon X has r sides, and each vertex has an angle measure of  [#permalink]

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21 Jul 2017, 06:27

Maximum angle for Polygon X can be 179, when the number of sides is 360( cannot be 180- it is a straight single line). Therefore polygon Q has 90 sides and hence interior angle is 176.

Note- Interior angle of a polygon is [((n-2)/ n ) x 180 ]. To get the largest integral value keep increasing n value such that denominator is the factor of numerator. Maximum value possible is 360. IF WE INCREASE FURTHER THE ANGLE VALUE WILL BE of format 179._ _ _
Regular polygon X has r sides, and each vertex has an angle measure of   [#permalink] 21 Jul 2017, 06:27
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