ShmoopTube

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Here’s your shmoop du jour, brought to you by hexagons.

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We don’t know what it is, but every time we're confronted with one of these things, we bolt.

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Line k bisects the angles of this regular hexagon that it intersects. Find x.

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Here are the potential answers...

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You may not see how this problem can possibly have any real life application…

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…but don’t come crying to us next time you and your friend have a hexagonal cake

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that you want to divide evenly between the two of you.

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All right, so let’s call line k the knife that’s being used to cut two completely equal, fair slices.

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For starters, how do we figure out how many angles there are in a hexagon?

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Well, we know there are 180 in a triangle…

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…and 360 in a square…

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…seems like we keep adding 180 degrees for each side we introduce.

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You can always use “number of sides minus 2 times 180” to find the total number of

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degrees in a polygon…

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…which, in this case, is 6 minus 2, or 4, times 180… which is 720.

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720 total degrees… divided among 6 angles… means that each angle is 120 degrees.

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But remember – our knife…er, line… is bisecting that angle…

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which slices it perfectly in half.

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Half of 120 is 60… and that’s the measure of angle x.

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Our solution is choice B.

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As in “Birthday cake for twins.”

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