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# In the figure above, the line segments meet at a point. If the point

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Math Expert
Joined: 02 Sep 2009
Posts: 47967
In the figure above, the line segments meet at a point. If the point  [#permalink]

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27 Jul 2017, 01:46
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Difficulty:

45% (medium)

Question Stats:

69% (01:26) correct 31% (01:39) wrong based on 89 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

Attachment:

2017-07-27_1245.png [ 23.28 KiB | Viewed 1307 times ]

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Re: In the figure above, the line segments meet at a point. If the point  [#permalink]

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27 Jul 2017, 03:35
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1
From the above figure, 6a + 3b = 360 because angle around a point is 360 degree

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

(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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Re: In the figure above, the line segments meet at a point. If the point  [#permalink]

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27 Jul 2017, 03:43
6A+3B= 360

2A+1B= 120 ( Ans - C)
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Re: In the figure above, the line segments meet at a point. If the point  [#permalink]

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27 Jul 2017, 03:48
Bunuel wrote:

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

Attachment:
2017-07-27_1245.png

We know
6a+3b = 360
2a+b = 120

Only Option C is 2a+b (RQU)

Hence C
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Re: In the figure above, the line segments meet at a point. If the point  [#permalink]

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06 Aug 2018, 11:40
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  [#permalink]

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07 Aug 2018, 11:55
Bunuel wrote:

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

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 = $$2a+b=120°$$

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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In the figure above, the line segments meet at a point. If the point &nbs [#permalink] 07 Aug 2018, 11:55
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