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# In the above figure, ABC, BD, BE, BF, BG and BH are all line segments.

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Math Expert
Joined: 02 Sep 2009
Posts: 54440
In the above figure, ABC, BD, BE, BF, BG and BH are all line segments.  [#permalink]

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01 Aug 2017, 04:45
00:00

Difficulty:

25% (medium)

Question Stats:

93% (01:26) correct 7% (00:52) wrong based on 45 sessions

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In the above figure, ABC, BD, BE, BF, BG and BH are all line segments. Which of the following angles may be determined in numbers of degrees?

(A) ∠ABH
(B) ∠ABG
(C) ∠ABF
(D) ∠GBE
(E) ∠EBC

Attachment:

2017-08-01_1348_002.png [ 12.86 KiB | Viewed 1039 times ]

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Joined: 22 May 2016
Posts: 2647
In the above figure, ABC, BD, BE, BF, BG and BH are all line segments.  [#permalink]

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06 Aug 2017, 12:55
1
Bunuel wrote:

In the above figure, ABC, BD, BE, BF, BG and BH are all line segments. Which of the following angles may be determined in numbers of degrees?

(A) ∠ABH
(B) ∠ABG
(C) ∠ABF
(D) ∠GBE
(E) ∠EBC

Attachment:
2017-08-01_1348_002.png

Given: ABC is a line segment.

ABC = 180°

Taking given measures of ALL angles:

4a + 2b = 180
Divide by 2
2a + b = 90

Angles ABF and FBC both equal 2a + b
We can determine, therefore, that those two angles have measures of 90 degrees.

∠FBC is not among the choices.

∠ABF, however, IS among the options in

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Joined: 15 Jan 2017
Posts: 351
Re: In the above figure, ABC, BD, BE, BF, BG and BH are all line segments.  [#permalink]

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08 Aug 2017, 02:05
ABF = 90
if we know this then the other angles also make sense in terms of measurement
Re: In the above figure, ABC, BD, BE, BF, BG and BH are all line segments.   [#permalink] 08 Aug 2017, 02:05
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