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which one of the following could be the value of b
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Updated on: 11 Dec 2016, 09:50
Updated on: 11 Dec 2016, 09:50
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Question Stats:
86% (01:57) correct
13% (01:47) wrong based on 15 sessions
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File comment: this is the diagram the question refers.
geometry.png [ 10.53 KiB | Viewed 3959 times ]
geometry.png [ 10.53 KiB | Viewed 3959 times ]
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
Re: geometry question
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11 Dec 2016, 08:16
11 Dec 2016, 08:16
1
Expert Reply
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.
Please mention the source of the question. And add tags
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.
Please mention the source of the question. And add tags
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Re: which one of the following could be the value of b
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27 Apr 2021, 15:34
27 Apr 2021, 15:34
ssiva wrote:
Attachment:
geometry.png
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
We know that all 5 angles in the circle must add to 360 degrees.
So, we can write: (a) + (b - a/2) + (a/2 + 2b) + (2a - 2b) + (2a - b) = 360
Simplify left side: 5a = 360
Solve: a = 72
So, we know the value of a BUT we don't know the value of b.
However, one thing we do know is that each angle must be greater than 0 degrees
So, for example, angle b cannot equal 20°, because we're told that one of the five angles is (b - a/2)
Since a = 72, this angle simplifies to be (b - 36)°
So, if b = 20, then that particular angle = (20 - 36)° = -16°, which is impossible. ELIMINATE A
Also, if b = 30, then that same angle = (30 - 36)° = -6°, which is impossible. ELIMINATE B
We also know that one of the angles = (2a - 2b)°
Since a = 72, this angle simplifies to be (144 - 2b)°
If b = 75, then this particular angle =(144 - 150)° = -6°, which is impossible. ELIMINATE D
Also, if b = 90, then this particular angle =(144 - 180)° = -36°, which is impossible. ELIMINATE E
By the process of elimination, the correct answer is C
Cheers,
Brent
