In a 12-sided regular polygon shown above, O is the center ...........

Question

https://e-gmat.com/blogs/wp-content/uploads/2018/12/Geo-2.png

In a 12-sided regular polygon shown above, O is the center of the polygon. What is the value of  \frac{a}{b} ?

A.  2
 B.  3
 C.  4
 D.  5
 E.  6

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

Chethan92 · Answer

Angle b = 360/12 = 30 degrees.
Then a/b = 150/30 = 5.

D is the answer.

Archit3110 · Answer

each interior angle 'a' = 180-360/n = 180-360/12= 180-30=150

and center angle would b = 360/12= 30

so ratio a/b = 150/30 = 5 IMO D

Appu087 · Answer

Sum of interior angle of polygon = n-2*180 = 1800
So sum of each angle = 1800/12 = 150 = a
Sum of all angles at the centre shall be 360 so b = 360/12 = 30
so a/b = 150/30 = 5

EgmatQuantExpert · Answer

Solution 
  Given:  
 • We are given a 12-sided regular polygon, and O is the center of the polygon

To find:  
 • We are asked to find the value of  \frac{a}{b}

Approach and Working:   
From the given figure, we can see that ‘a’ is the interior angle of the regular polygon,
 • We know that, interior angle of an n-sided regular polygon =  180 * \frac{(n – 2)}{n} , 
o From this, we get,  a = 180 * \frac{(12 - 2)}{12} = 150^o

We can also infer that  b = \frac{360}{n} , where n is the number of sides of the polygon
 • Since, there can be ‘n’ such triangles formed inside the polygon, and sum of all the angles at the center =  360^o 
• Thus,  b = \frac{360}{12} = 30^o

Therefore, the value of  \frac{a}{b} = \frac{150}{30} = 5

Hence the correct answer is Option D.

Answer: D

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Quant-workshop_Webinar-e1533628475738.jpg

bumpbot · Answer

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In a 12-sided regular polygon shown above, O is the center ...........

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In a 12-sided regular polygon shown above, O is the center ...........

Prep Toolkit

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