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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 ...........  [#permalink]

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New post 05 Dec 2018, 00:13
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D
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In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

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New post 05 Dec 2018, 00:31
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Angle b = 360/12 = 30 degrees.
Then a/b = 150/30 = 5.

D is the answer.
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Re: In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

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New post 05 Dec 2018, 00:46
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EgmatQuantExpert wrote:
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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

Image



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
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Re: In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

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New post 05 Dec 2018, 01:31
1
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
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In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

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New post 10 Dec 2018, 01:03

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

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Re: In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

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Re: In a 12-sided regular polygon shown above, O is the center ...........   [#permalink] 02 Apr 2020, 08:44

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

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