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anceer
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
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Question Stats:
39% (02:31) correct
61%
(02:57)
wrong
based on 177
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In the diagram above, angles GAF, FBE, and ECD are all equal in measure. If line AG is the diameter of the circle and parallel to lines BF and CE, what is the measure of angle CFB?
A. 15
B. 20
C. 25
D. 30
E. 35
Attachment:
Untitled.png [ 14.45 KiB | Viewed 10706 times ]
05 Dec 2014, 07:42
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Let "O" be the center of the circle
Angle AOG=180
Arcs GF=FE=ED=DC=CD=BA
Total: 6 arcs
180/6=30
So angles GOF=FOE=EOD=DOC=COB=BOA=30
Inscribed angles measure half of their corresponding central angles = 30/2 = 15
Angle AOG=180
Arcs GF=FE=ED=DC=CD=BA
Total: 6 arcs
180/6=30
So angles GOF=FOE=EOD=DOC=COB=BOA=30
Inscribed angles measure half of their corresponding central angles = 30/2 = 15
General Discussion
anceer
Joined: 04 Aug 2013
Last visit: 18 Sep 2023
Posts: 79
Own Kudos:
Given Kudos: 56
Location: India
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GMAT 1: 670 Q47 V35
GPA: 3
WE:Manufacturing and Production (Pharmaceuticals and Biotech)
05 Dec 2014, 05:59
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The OE
Can any one explain it..
A. This problem relies heavily on the concepts of inscribed and central angles. If all the inscribed angles in the figure (GAF, FBE, ECD, and their "opposite" angles across the circle) are the same measurement, then there are 6 identical inscribed angles in the semicircle. Now, consider if each arclength - AB, BC, CD, etc. - were created by central angles. That would be six 30-degree angles from the center of the circle, and since inscribed angles measure half of their corresponding central angles, that means that the inscribed angles are 15 degrees, making A the correct answer.
Can any one explain it..
A. This problem relies heavily on the concepts of inscribed and central angles. If all the inscribed angles in the figure (GAF, FBE, ECD, and their "opposite" angles across the circle) are the same measurement, then there are 6 identical inscribed angles in the semicircle. Now, consider if each arclength - AB, BC, CD, etc. - were created by central angles. That would be six 30-degree angles from the center of the circle, and since inscribed angles measure half of their corresponding central angles, that means that the inscribed angles are 15 degrees, making A the correct answer.
