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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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26 Apr 2019, 02:23
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60% (01:35) correct 40% (01:21) wrong based on 465 sessions

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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 [ 10.02 KiB | Viewed 3555 times ]

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

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27 Apr 2019, 05:53
3
2
Bunuel wrote:

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

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

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26 Apr 2019, 02:41
3
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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27 Apr 2019, 06:56
1
Bunuel wrote:

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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29 Apr 2019, 11:34
1
Top Contributor
Bunuel wrote:

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

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

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06 May 2019, 20:21
Bunuel wrote:

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.

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

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Updated on: 11 Jul 2019, 11:35
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 rules 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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Originally posted by EMPOWERgmatRichC on 13 May 2019, 13:15.
Last edited by EMPOWERgmatRichC on 11 Jul 2019, 11:35, edited 1 time in total.
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In the figure above, RST is a triangle with angle measures as shown an  [#permalink]

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10 Jul 2019, 10:37
Why can we not assume that r is equivalent to t since sides ST and SR appear equivalent, hence allowing us to solve for (X+Y)?
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Re: In the figure above, RST is a triangle with angle measures as shown an  [#permalink]

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11 Jul 2019, 01:59
1
Even before looking at options 1&2,

We can calculate:

x+r+y+t=360; 360-r-t=x+y ------------------------eq.1

r+t+s=180 ; 180-r-t = s -----------------eq.2

For eq.2 if we add 180 on both sides, we get 360-r-t = 180+s -------------------eq.3

from eq.1 and eq.3, we get 180+s = x+y.

So, we only need the option which has the value of s in it to calculate x+y.

so (1) is sufficient.

Consider Statement (2)

r alone is not going to be sufficient because s will always influence t's value and without knowing s, we cant find x+y. So individual values of X&Y need to be found, which is not possible without using (1) also.

So 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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11 Jul 2019, 11:38
1
Hi Eagles1795,

When dealing with pictures of shapes in DS questions, we CANNOT assume that the picture is 'drawn to scale.' Thus, while ST and SR might be the same length (meaning that angles r and t are equal), it's possible that one of those sides is longer than the other (meaning that angles r and t are NOT equal). With DS questions, we will ALWAYS need more information to answer the question than the initial prompt provides. In my post (directly above yours), I explain how to get to the correct answer.

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Re: In the figure above, RST is a triangle with angle measures as shown an   [#permalink] 11 Jul 2019, 11:38
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