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# In the regular hexagon above, what is x?

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In the regular hexagon above, what is x?  [#permalink]

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10 May 2015, 05:28
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Difficulty:

25% (medium)

Question Stats:

73% (01:32) correct 27% (02:02) wrong based on 54 sessions

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In the regular hexagon above, what is x?

A. 100°
B. 108°
C. 120°
D. 135°
E. 144°
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Joined: 24 Jun 2008
Posts: 1829
Re: In the regular hexagon above, what is x?  [#permalink]

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10 May 2015, 05:44
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1
In an n-sided shape, the angles always sum to (n-2)(180). So in a hexagon, with 6 sides, the angles sum to (6-2)(180) = 720. In a regular hexagon, all six angles are equal, so every angle is 720/6 = 120 degrees.

I'll label the corners of the hexagon A, B, C, D, E and F, going clockwise from the leftmost point. In the diagram, a line is drawn connecting A and C. Notice this makes an isosceles triangle (since the edges of a regular hexagon are all the same) with an angle of 120 degrees at point B. Since the triangle is isosceles, the other two angles must be equal, and since the angles in a triangle always add to 180, the other two angles must each be 30 degrees. You'll find the same angles in the triangle made by connecting points B and D.

So the small triangle at the very top of our diagram has two 30 degree angles, so the remaining angle in that triangle (opposite the 'x') is 120 degrees. Since x is opposite that 120 degree angle in an X-pattern, then x is also 120 degrees.
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Re: In the regular hexagon above, what is x?  [#permalink]

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10 May 2015, 06:22
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120

Very easy question. Very gmat type.
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Re: In the regular hexagon above, what is x?   [#permalink] 10 May 2015, 06:22
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