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605-655 (Medium)|   Geometry|      
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Bunuel
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In the figure above, the line segments meet at a point. If the point 27 Jul 2017, 01:46
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66% (01:57) correct 34% (02:00) wrong based on 151 sessions

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In the figure above, the line segments meet at a point. If the point is named Q, which of the following angles has a degree measure that can be determined?

(A) RQS
(B) RQT
(C) RQU
(D) RQV
(E) RQW


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2017-07-27_1245.png
2017-07-27_1245.png [ 23.28 KiB | Viewed 4278 times ]
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C
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In the figure above, the line segments meet at a point. If the point 27 Jul 2017, 03:35
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From the above figure, 6a + 3b = 360 because angle around a point is 360 degree

Therefore, 3(2a + b) = 360 => 2a + b = 120

Going by answer options
(A) RQS = b
(B) RQT = a + b
(C) RQU = 2a + b
(D) RQV = 3a + b
(E) RQW = 3a + 2b

Only Option C(RQU) = 2a + b is known and is our correct answer.
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In the figure above, the line segments meet at a point. If the point 27 Jul 2017, 03:43
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6A+3B= 360

2A+1B= 120 ( Ans - C)
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In the figure above, the line segments meet at a point. If the point 27 Jul 2017, 03:48
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Bunuel

In the figure above, the line segments meet at a point. If the point is named Q, which of the following angles has a degree measure that can be determined?

(A) RQS
(B) RQT
(C) RQU
(D) RQV
(E) RQW


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Attachment:
2017-07-27_1245.png
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We know
6a+3b = 360
2a+b = 120

Only Option C is 2a+b (RQU)

Hence C
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In the figure above, the line segments meet at a point. If the point 06 Aug 2018, 11:40
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Here we have nine angles. If we cluster them like this way (b + 2a) + (b + 2a) + (b + 2a) we can notice that b + 2a equals 1/3 of 360. RQU is exactly b + 2a. So option C.
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In the figure above, the line segments meet at a point. If the point 07 Aug 2018, 11:55
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Bunuel

In the figure above, the line segments meet at a point. If the point is named Q, which of the following angles has a degree measure that can be determined?

(A) RQS
(B) RQT
(C) RQU
(D) RQV
(E) RQW

Show more
If stuck, start with what you know.
The sum of all angles around a point is 360°. (The angles make a circle = 360°) How many angles = \(a\)? How many angles = \(b\)? Count each kind and sum. \(6a +3b=360°\)

Now what? With one equation and two variables, we cannot solve for either variable. Thus, our "measurable angle" will be defined by both \(a\) and \(b\).

Because our answer will contain both variables, we need some (_a + _b) expression. The original equation is our only source. It must be amenable to manipulation. It is. Divide the equation
\(6a +3b=360°\) by \(3\)
\(2a+b=120°\)

So we need an angle composed of one \(b\) and two \(a\)'s. Answer choices require us to start at R. Moving clockwise from R, we do not have much choice.

The first angle between R and S = \(b\)
The next angle between S and T = \(a\)
The next angle between T and U = \(a\)
Angle RQU = \(2a+b=120°\)

Answer C

You can check the other answers if uncertain. The angles in A, B, D, and E respectively are composed of (b), (a+b), (3a+b), and (3a+2b) -- NOT (2a+b).
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