What is the number of sides of a regular polygon in which 1/3rd of the

Question

What is the number of sides of a regular polygon in which 1/3rd of the sum of exterior angle is equal to the each interior angle ?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 8

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satya2029 · Answer

the sum of the measures of the exterior angles of a polygon is always 360°.
Each internal angle= 360/3=120 for n side it will be 120n
sum of internal angle=](n-2)*180]/n
120n=180n-360
n=6
D:)

CareerGeek · Answer

Each interior angle of a regular polygon =  \frac{180(n - 2)}{n} 
& sum of exterior angles of any n-sided polygon = 360

Given,  \frac{1}{3}*360 = \frac{180(n - 2)}{n} 
-->  120 = \frac{180(n - 2)}{n} 
-->  120n = 180n - 360 
-->  360 = 180n - 120n = 60n 
-->  n = \frac{360}{60} = 6

Option D

GMATinsight · Answer

CONCEPT : 
Exterior angle of a polygon = 360/n where n is the number of sides of a polygon
Interior angle of a polygon = 180- (360/n)
Sum of exteriorangles in any polygon = 360

i.e. Given, (1/3)*360 = 180- (360/n)

i.e. n = 6

Answer: Option D

lacktutor · Answer

The sum of the interior angles - 180º(n-2)
The sum of the interior angles- 2π= 360º

\frac{180*(n-2)}{n} = (\frac{1}{3})*2π

\frac{(n-2)}{n}= \frac{2}{3}

3n -6= 2n 
-->  n=6

The answer is D.

exc4libur · Answer

The sum of the exterior angles of any polygon is 360;
The sum of the interior angles of an n-sided polygon is 180(n-2);
1/3*360=120: 180(n-2)/n=120, n=6

Ans (D)

ScottTargetTestPrep · Answer

The sum of the measures of the exterior angles of any polygon is 360 degrees. The measure of each interior angle of an n-sided regular polygon is 180(n - 2)/n degrees. Therefore, we can create the equation:

180(n - 2)/n = ⅓(360)

(180n - 360)/n = 120

180n - 360 = 120n

60n = 360

n = 6

Answer: D

Kinshook · Answer

Asked: What is the number of sides of a regular polygon in which 1/3rd of the sum of exterior angle is equal to the each interior angle ?

Sum of exterior angle = 2*180 = 360
1/3rd of the sum of exterior angle = 360/3 = 120

Let the number of sides of the polygon be n

Interior angle = 180(n-2)/n = 120 
n-2/n = 120/180 = 2/3
n = 6

Number of sides = n = 6

IMO D

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What is the number of sides of a regular polygon in which 1/3rd of the

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