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03 Sep 2018, 05:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
61% (01:37) correct
39%
(02:20)
wrong
based on 18
sessions
History
Date
Time
Result
Not Attempted Yet
If ABCDEFGH is an octagon with all sides equal, such that ∠ABC = ∠BCD = ∠CDE = ∠DEF = ∠EFG = ∠FGH = ∠GHA = ∠HAB, how many degrees is ∠GBC?
A. \(45\)
B. \(67.5\)
C. \(90\)
D. \(120\)
E. \(135\)
A. \(45\)
B. \(67.5\)
C. \(90\)
D. \(120\)
E. \(135\)
03 Sep 2018, 05:30
Kudos
Bookmarks
Official Solution:
If ABCDEFGH is an octagon with all sides equal, such that ∠ABC = ∠BCD = ∠CDE = ∠DEF = ∠EFG = ∠FGH = ∠GHA = ∠HAB, how many degrees is ∠GBC?
A. \(45\)
B. \(67.5\)
C. \(90\)
D. \(120\)
E. \(135\)
We’ll go for ALTERNATIVE because in regular polygons we can use symmetry.
Since the question tells us that all sides and all angles are equal, we know we are dealing with a regular polygon. If we draw a regular octagon and add line BG to it, we can SEE that ∠GBC = ∠BGF, because of symmetry, which means that each of the two is 90˚.
Answer: C
If ABCDEFGH is an octagon with all sides equal, such that ∠ABC = ∠BCD = ∠CDE = ∠DEF = ∠EFG = ∠FGH = ∠GHA = ∠HAB, how many degrees is ∠GBC?
A. \(45\)
B. \(67.5\)
C. \(90\)
D. \(120\)
E. \(135\)
We’ll go for ALTERNATIVE because in regular polygons we can use symmetry.
Since the question tells us that all sides and all angles are equal, we know we are dealing with a regular polygon. If we draw a regular octagon and add line BG to it, we can SEE that ∠GBC = ∠BGF, because of symmetry, which means that each of the two is 90˚.
Answer: C
11 Aug 2025, 19:23
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Automated notice from GMAT Club BumpBot:
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A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
