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The figure shows the rectangle ABCD. What is ∠x - ∠y?

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Math Revolution GMAT Instructor
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The figure shows the rectangle ABCD. What is ∠x - ∠y?  [#permalink]

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New post 23 Oct 2019, 01:21
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (02:28) correct 14% (02:27) wrong based on 37 sessions

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[GMAT math practice question]

The figure shows the rectangle \(ABCD.\) What is \(∠x - ∠y\)?

\(A. 20^o\)

\(B. 17^o\)

\(C. 15^o\)

\(D. 13^o\)

\(E. 12^o\)

Attachment:
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10.23PS.png [ 20.7 KiB | Viewed 281 times ]

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Re: The figure shows the rectangle ABCD. What is ∠x - ∠y?  [#permalink]

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New post 23 Oct 2019, 02:38
1
APB=90-15=75
DPQ= 90-y

75+x+90-y= 180
x-y=15


MathRevolution wrote:
[GMAT math practice question]

The figure shows the rectangle \(ABCD.\) What is \(∠x - ∠y\)?

\(A. 20^o\)

\(B. 17^o\)

\(C. 15^o\)

\(D. 13^o\)

\(E. 12^o\)

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The attachment 10.23PS.png is no longer available

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Untitled.png [ 5.39 KiB | Viewed 249 times ]

Math Revolution GMAT Instructor
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V
Joined: 16 Aug 2015
Posts: 8149
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The figure shows the rectangle ABCD. What is ∠x - ∠y?  [#permalink]

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New post 25 Oct 2019, 01:09
=>

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Since \(AP, RP\) and \(CD\) are parallel, we have \(<ABP = <BPR\) and \(<DQP = <RPQ\). Since \(<BPQ = <BPR + <RPQ,\) we have \(<x = 15° + <y.\)

So, we have \(<x - <y = 15°\).

Therefore, C is the answer.
Answer: C
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Re: The figure shows the rectangle ABCD. What is ∠x - ∠y?   [#permalink] 25 Oct 2019, 01:09
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