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# M70-22

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Math Expert
Joined: 02 Sep 2009
Posts: 58445

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03 Sep 2018, 05:30
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Question Stats:

67% (03:44) correct 33% (02:01) wrong based on 3 sessions

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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. $$135$$

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Math Expert
Joined: 02 Sep 2009
Posts: 58445

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03 Sep 2018, 05:30
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˚.

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Re M70-22   [#permalink] 03 Sep 2018, 05:30
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# M70-22

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