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In the figure above, RST is a triangle with angle measures as shown an

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In the figure above, RST is a triangle with angle measures as shown an  [#permalink]

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New post 26 Apr 2019, 02:23
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (01:40) correct 41% (01:35) wrong based on 120 sessions

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Re: In the figure above, RST is a triangle with angle measures as shown an  [#permalink]

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New post 26 Apr 2019, 02:41
Should be a, x+y would be equal to r+2s+t
R+2s+t= r+t+s+s= 180+s, hence option a

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Re: In the figure above, RST is a triangle with angle measures as shown an  [#permalink]

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New post 27 Apr 2019, 05:53
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Bunuel wrote:
Image
In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y ?

(1) s = 40
(2) r = 70


DS63602.01
OG2020 NEW QUESTION


The original question: \(x+y=?\) Imagine x and y as angle measures of supplementary angles.
The rephrased question: \((180-r)+(180-t)=? \implies 360-(r+t)=? \implies r+t=?\)

1) We know that \(s=40\) and \(r+t+s=180\), so \(r+t=140\). Thus, the answer to the rephrased question is a unique value. \(\implies\) Sufficient

2) We know that \(r=70\), and all we can infer is that \(70<r+t<180\). Thus, we can't get a unique value to answer the rephrased question. \(\implies\) Insufficient

Answer: A
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Re: In the figure above, RST is a triangle with angle measures as shown an  [#permalink]

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New post 27 Apr 2019, 06:56
Bunuel wrote:
Image
In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y ?

(1) s = 40
(2) r = 70


DS63602.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1321.png


from given info
x=s+t
y=s+r
and s+t+r = 180
t+r= 140
and x+y= 2s+t+r
so x+y = 80+140 ; 220
sufficient
from2 r=70 , insufficeint
IMO A
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Re: In the figure above, RST is a triangle with angle measures as shown an  [#permalink]

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New post 29 Apr 2019, 11:34
Top Contributor
Bunuel wrote:
Image
In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y ?

(1) s = 40
(2) r = 70
Attachment:
2019-04-26_1321.png

Given: RST is a triangle with angle measures as shown and PRTQ is a line segment

Target question: What is the value of x + y ?

Statement 1: s = 40
Since angles in a triangle add to 180°, we know that r° + t° = 140°
Since angles on a line add to 180°, we know that x° + r° = 180°, and we know that t° + y° = 180°
So, we can write: x° + r° + t° + y° = 180° + 180°
Rearrange: x° + y° + r° + t° = 360°
Substitute to get: x° + y° + 140° = 360°
Subtract 140° from both sides to get: x° + y° = 220°
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: r = 70
This tells us that x° = 110°, however we have no information about the value of any other angle.
Statement 2 is NOT SUFFICIENT

Answer: A

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Re: In the figure above, RST is a triangle with angle measures as shown an  [#permalink]

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New post 06 May 2019, 20:21
Bunuel wrote:
Image
In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y ?

(1) s = 40
(2) r = 70


DS63602.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1321.png


Since x and y are exterior angles or r and t respectively, we can represent x and y as 180 - r and 180 - t.
So we need to determine (180 - r) + (180 - t) = 360 - r - t = 360 - (r + t)

Statement One Alone:

s = 40

Since = 40, r + t = 180 - 40 = 140.

Thus, x + y = 360 - 140 = 220.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

r = 70

We see that x is 180 - 70 = 110.

However, we can’t determine the value of y since we don’t know the value of t or s. Statement two alone is not sufficient to answer the question.

Answer: A
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Re: In the figure above, RST is a triangle with angle measures as shown an  [#permalink]

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New post 13 May 2019, 13:15
Hi All,

We're told that In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. We're asked for the value of (X+Y). This question is built around a couple of Geometry lines involving Triangles and Lines. To start, the angles in the triangle (re: s, r and t) total 180 degrees and so do the pairs of angles (x+r) = 180 and (t+y) = 180.

(1) s = 40

With angle s, we know that r+t must total 140 degrees. Those two angles are part of the two 180 degree totals on the line, meaning that r+t+x+y = 360 degrees. We now know that r+t = 180, so....
r+t+x+y = 360
180+x+y = 360
x+y = 180
Fact 1 is SUFFICIENT

(2) r = 70

Fact 2 helps us to determine the value of angle x (since x+r = 180, we know that x = 110 degrees), but we don't know the value of y.
Fact 2 is INSUFFICIENT

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Re: In the figure above, RST is a triangle with angle measures as shown an   [#permalink] 13 May 2019, 13:15
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