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

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Math Expert
Joined: 02 Sep 2009
Posts: 46301
In the figure above, what is r + s in terms of x? [#permalink]

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22 Aug 2017, 08:50
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Difficulty:

25% (medium)

Question Stats:

93% (01:00) correct 7% (01:55) wrong based on 65 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

Attachment:

2017-08-22_1947.png [ 6.77 KiB | Viewed 707 times ]

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Re: In the figure above, what is r + s in terms of x? [#permalink]

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22 Aug 2017, 09:10
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Clearly answer is A : x
solution is attached.
Attachments

IMG_0732.JPG [ 1.68 MiB | Viewed 526 times ]

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Re: In the figure above, what is r + s in terms of x? [#permalink]

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22 Aug 2017, 09:12
(90-x)+s+r+90=180

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

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In the figure above, what is r + s in terms of x? [#permalink]

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22 Aug 2017, 12:44
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

Attachment:
2017-08-22_1947.png

Angles sum to 180

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

$$r + s + 90 - x + 90 = 180$$

$$r + s - x = 0$$

$$r + s = x$$

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Re: In the figure above, what is r + s in terms of x? [#permalink]

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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

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

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Re: In the figure above, what is r + s in terms of x? [#permalink]

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24 Aug 2017, 16:04
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

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

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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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