ShmoopTube

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

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Specifically – Romano, Lewis and Charles. Not sure what they were doing hanging out together.

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A certain angle equals n degrees If ray BD bisects angle ABC, ray BF bisects

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angle DBC, ray BG bisects angle FBC, and ray BE bisects angle DBG, what is the measurement

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of angle EBC in terms of n?

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And here are the potential answers:

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Okay, yeah – we get the warning that the figure was “not drawn to scale”

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…but it's like this diagram was apparently drawn by a six year old.

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We’re going to draw our own diagram. And it’s going to be amazing.

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BD bisects our original angle, so ABD and DBC are equal.

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BF bisects DBC, so both DBF and FBC must be one-half the measure of n. So far so good.

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Same deal with BG, which bisects FBC… which means that now both FBG and GBC are one-fourth

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the measure of n.

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Now here's where it gets tricky. BE bisects DBG.

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Well, we know the measure of DBC – one n… and we know the measure of GBC – one-fourth n.

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The angle DBG must then be the difference – or three-fourths n.

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Because BE is bisecting THAT angle… EBC must be half of three-fourths – or three-eighths

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– plus angle GBC right here.

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Three-eighths plus one-fourth – or, simplified, three-eighths plus two-eighths, is five-eighths.

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And that's it...Answer D.

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