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SAT Math 3.3 Geometry and Measurement
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?
Full Transcript
- 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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