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which one of the following could be the value of b

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which one of the following could be the value of b [#permalink] New post 11 Dec 2016, 06:03
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File comment: this is the diagram the question refers.
geometry.png
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From the figure, which one of the following could be the value of b ?
(A) 20
(B) 30
(C) 60
(D) 75
(E) 90

thank you
siva
[Reveal] Spoiler: OA

Last edited by Carcass on 11 Dec 2016, 09:50, edited 1 time in total.
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Re: geometry question [#permalink] New post 11 Dec 2016, 08:16
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The sum of the angles in a circle is 360.

Now we write down the values one by one:

\(a + b - \frac{a}{2} + \frac{a}{2} + 2b + 2a - 2b + 2a - b\) \(=360\)
\(a + b + 2a + 2a - b\) \(=360\)

\(a + 2a + 2a\) \(=360\)
\(5a\) \(=360\) So we can find value of a = 72.

Now we assume that all the values of angles are positive

\(2a - b \geq 0\) or \(b \leq 144\)

\(b - \frac{a}{2} \geq 0\) or \(b \geq 36\)

Finally \(2a - 2b \geq 0\) so \(b \leq 72\).

So all option with values of b between 36 and 72 are possible.

Hence option C is correct.

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Re: geometry question   [#permalink] 11 Dec 2016, 08:16
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which one of the following could be the value of b

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