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A and B are the endpoints of a line segment. Segment AB is crossed thr

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
A and B are the endpoints of a line segment. Segment AB is crossed thr  [#permalink]

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30 Oct 2018, 03:30
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Difficulty:

45% (medium)

Question Stats:

68% (02:13) correct 32% (01:43) wrong based on 42 sessions

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A and B are the endpoints of a line segment. Segment AB is crossed through point C by another line segment with endpoints D and E. If ∠ACD > 90?, and the sum of ∠ACE and ∠BCD is x, then which of the following must be true?

A. x < 90
B. x > 90
C. 90 < x < 180
D. x < 180
E. x > 180

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Joined: 24 Jun 2013
Posts: 144
Location: India
Schools: ISB '20, GMBA '20
Re: A and B are the endpoints of a line segment. Segment AB is crossed thr  [#permalink]

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30 Oct 2018, 20:12
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Bunuel wrote:
A and B are the endpoints of a line segment. Segment AB is crossed through point C by another line segment with endpoints D and E. If ∠ACD > 90?, and the sum of ∠ACE and ∠BCD is x, then which of the following must be true?

A. x < 90
B. x > 90
C. 90 < x < 180
D. x < 180
E. x > 180

if we conceptualise the image then angle ACD & angle ECB would be vertically opp angle and hence equal; as ACD >90 so must be ECB, therefore their total should be >180;
now the other two vertically opp angle namely ACE & BCD (together = x) x should be < 180 (as total should be 360)

D
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Re: A and B are the endpoints of a line segment. Segment AB is crossed thr   [#permalink] 30 Oct 2018, 20:12
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