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# What is the perimeter of a regular polygon with sides of len

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What is the perimeter of a regular polygon with sides of len  [#permalink]

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12 Jun 2014, 22:39
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What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm
B. 108 cm
C. 120 cm
D. 132 cm
E. 144 cm
Manager
Joined: 17 Nov 2013
Posts: 73
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GMAT 1: 710 Q49 V38
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Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

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12 Jun 2014, 23:23
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Summation of interior angles is given by:
180(N-2) = interior angle * N
N: no of sides

180(N-2) = 144N
180N - 360 = 144N
36N = 360
N = 10

Perimeter:
N * length of side = 10 * 12 = 120

C

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Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

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16 Jun 2014, 03:36
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phlaym39 wrote:
What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm
B. 108 cm
C. 120 cm
D. 132 cm
E. 144 cm

Sum of all interior angles is given by:
180(n-2) = n is number of sides

180(n-2) = 144*n
from here
n = 10

So perimeter becomes 12*10= 120 answer
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Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

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01 Oct 2014, 02:51
Interior angle = 144

Its a decagon (Polygon with 10 sides)

Formula to find sides is same as shown in above posts

Perimeter = 10 * 12 = 120

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Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

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19 May 2017, 23:37
For any polygon, sum of its interior and exterior angle (at that particular vertex) = 180
If interior angle = 144, exterior angle = 180-144 = 36

For a regular polygon of n sides, each exterior angle = 360/n (sum of all exterior angles of a polygon is 360)
So 360/n = 36 or n = 10.

Perimeter of regular polygon = n* length of each side = 10*12 = 120

Hence C
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Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

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22 May 2017, 15:40
phlaym39 wrote:
What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm
B. 108 cm
C. 120 cm
D. 132 cm
E. 144 cm

Let number of sides of the polygon be n. (Given its a regular polygon. Regular polygon has all sides and interior angles equal.)

Internal Angle = $$\frac{180 (n-2)}{n}$$

Given internal Angle is $$144^{\circ}$$

Therefore; $$\frac{180 (n-2)}{n}$$ = $$144^{\circ}$$

180 (n-2) = 144 x n

180n - 180 x 2 = 144n

180n - 144n = 180 x 2

36n = 180 x 2

n = $$\frac{180 x 2}{36}$$ = 10

Therefore total number of sides = 10.

Length of side is given = 12cm

Perimeter = 12 x 10 = 120 cm

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Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

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27 Apr 2018, 05:30
Top Contributor
phlaym39 wrote:
What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm
B. 108 cm
C. 120 cm
D. 132 cm
E. 144 cm

Sum of ALL sides in an n-sided polygon = (n - 2)(180) degrees

So, EACH ANGLE in a regular n-sided polygon = (n - 2)(180)/n degrees

We're told that EACH ANGLE is 144°, so we can write: (n - 2)(180)/n = 144
Multiply both sides by n to get: (n - 2)(180) = 144n
Expand left side: 180n - 360 = 144n
Add 360 to both sides: 180n = 144n + 360
Subtract 144n from both sides: 36n = 360
Solve: n = 10

This tells us that the polygon has 10 sides
Since each side is the SAME LENGTH in a REGULAR polygon, the perimeter = (10)(12 cm) = 120 cm

Cheers,
Brent
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Re: What is the perimeter of a regular polygon with sides of len  [#permalink]

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30 Apr 2018, 15:41
phlaym39 wrote:
What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 144° each?

A. 96 cm
B. 108 cm
C. 120 cm
D. 132 cm
E. 144 cm

We need to determine the number of sides of this regular polygon first before we can determine its perimeter. Let’s use the formula for sum of interior angles to determine the number of angles (and thus the number of sides) of the polygon. Recall that if a polygon has n sides, the total number of degrees of the interior angles is given by 180(n - 2). Since we are given that each interior angle measures 144 degrees, the total number of degrees of the interior angles is also 144n. Thus we can create the equation:

144n = 180(n - 2)

144n = 180n - 360

360 = 36n

10 = n

Thus, the perimeter is 10 x 12 = 120.

Alternate Solution:

An exterior angle of this polygon is 180 - 144 = 36 degrees. Since exterior angles of a polygon always add up to 360, this polygon has 360 / 36 = 10 angles; which also means this polygon has 10 sides. Since each side measures 12 cm, the perimeter is 12 x 10 = 120 cm.

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Re: What is the perimeter of a regular polygon with sides of len &nbs [#permalink] 30 Apr 2018, 15:41
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# What is the perimeter of a regular polygon with sides of len

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