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In the figure above, what is r + s in terms of x?

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Bunuel
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In the figure above, what is r + s in terms of x? [#permalink] New post   22 Aug 2017, 08:50
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A
B
C
D
E

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5% (low)

Question Stats:

89% (01:13) correct 11% (01:33) wrong based on 78 sessions
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In the figure above, what is r + s in terms of x?

(A) x
(B) 2x
(C) 90 – x
(D) 90 – 2x
(E) 180 – 2x

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2017-08-22_1947.png
2017-08-22_1947.png [ 6.77 KiB | Viewed 1947 times ]
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A
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Re: In the figure above, what is r + s in terms of x? [#permalink] New post   22 Aug 2017, 09:10
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Clearly answer is A : x
solution is attached.
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Re: In the figure above, what is r + s in terms of x? [#permalink] New post   22 Aug 2017, 09:12
(90-x)+s+r+90=180

180-x+r+s=180
r+s=x

Answer A
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In the figure above, what is r + s in terms of x? [#permalink] New post   22 Aug 2017, 12:44
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Bunuel wrote:

In the figure above, what is r + s in terms of x?

(A) x
(B) 2x
(C) 90 – x
(D) 90 – 2x
(E) 180 – 2x

Show Spoiler
Attachment:
2017-08-22_1947.png

Angles sum to 180

\(r + s + (90 - x) + 90 = 180\)

\(r + s + 90 - x + 90 = 180\)

\(r + s - x = 0\)

\(r + s = x\)

Answer A
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Re: In the figure above, what is r + s in terms of x? [#permalink] New post   22 Aug 2017, 20:02
Bunuel wrote:

In the figure above, what is r + s in terms of x?

(A) x
(B) 2x
(C) 90 – x
(D) 90 – 2x
(E) 180 – 2x

Show Spoiler
Attachment:
2017-08-22_1947.png


The third angle in triangle that contains right angle and (90-x) is
180 - 90 -(90-x)
= x

r+s= x since exterior angle is equal to sum of interior opposite angles

Answer A
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Re: In the figure above, what is r + s in terms of x? [#permalink] New post   24 Aug 2017, 16:04
Expert Reply
Bunuel wrote:

In the figure above, what is r + s in terms of x?

(A) x
(B) 2x
(C) 90 – x
(D) 90 – 2x
(E) 180 – 2x

Show Spoiler
Attachment:
2017-08-22_1947.png


The large right triangle has 180 degrees. We can create the following equation:

r + s + (90 - x) + 90 = 180

r + s - x + 180 = 180

r + s - x = 0

r + s = x

Answer: A
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Re: In the figure above, what is r + s in terms of x? [#permalink]
24 Aug 2017, 16:04
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