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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
In the above figure, which one of the following COULD
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13 Jan 2019, 11:10
13 Jan 2019, 11:10
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In the above figure, which one of the following COULD be the value of b ?
(A) 20
(B) 30
(C) 60
(D) 75
(E) 90
Re: In the above figure, which one of the following COULD
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13 Jan 2019, 19:02
13 Jan 2019, 19:02
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GreenlightTestPrep wrote:
In the above figure, which one of the following COULD be the value of b ?
(A) 20
(B) 30
(C) 60
(D) 75
(E) 90
The sum of all angles must be 369°, so add all of them..
\(a+b-\frac{a}{2}+\frac{a}{2}+2b+2a-2b+2a-b=360....5a=360...a=72\)..
Now a is 60 and all angles given should be non-negative..
1) \(b-\frac{a}{2}\geq{0}...b\geq{36}\)
2)\(2a-2b\geq{0}.....b\leq{a}.....b \leq{72}\)
So \(36\leq{b}\leq{72}\)
Only, 60 fits in the range..
C
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the above figure, which one of the following COULD
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14 Jan 2019, 06:37
14 Jan 2019, 06:37
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GreenlightTestPrep wrote:
In the above figure, which one of the following COULD be the value of b ?
(A) 20
(B) 30
(C) 60
(D) 75
(E) 90
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
