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SAT Math 3.3 Geometry and Measurement 188 Views


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SAT Math 3.3 Geometry and Measurement


Transcript

00:02

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

00:06

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

00:13

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

00:22

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

00:35

of angle EBC in terms of n?

00:37

And here are the potential answers:

00:41

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

00:44

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

00:47

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

00:51

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

00:57

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

01:05

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

01:12

the measure of n.

01:13

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

01:19

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

01:26

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

01:30

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

01:36

– plus angle GBC right here.

01:39

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

01:45

And that's it...Answer D.

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