Help....

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Time wrote on 2010-12-16 21:32

In triangle ABC what is the sum of the degree measures of the six numbered angles_______

[Image: http://img607.imageshack.us/img607/7290/helpdy.jpg]

You cant assume anything. All I know is that somehow you have to get the answer knowing that triangle add up to 180 degrees and any theorem or rule that help you finish...

Its part of a packet, but I cant figure this one out for some reason.....
Kueh wrote on 2010-12-16 21:35

It's 180 times 3, minus 180.

Or 180 times 2

Or 360 degrees.

Want me to show why? Or is that enough?
Time wrote on 2010-12-16 21:45

Quote from Whyrainfalls;250036:
It's 180 times 3, minus 180.

Or 180 times 2

Or 360 degrees.

Want me to show why? Or is that enough?

I really dont get how it would be that...So it would help me a lot if you could explain lol. The rest of the packet seems to be making sense though, I hope I dont run into another one I just dont see like this one...
Akemii wrote on 2010-12-16 21:46

i love Geometry, but this hurts my head.
Kueh wrote on 2010-12-16 21:51

Gimme a minute so I can explain it with pictures.
Time wrote on 2010-12-16 22:00

Quote from Whyrainfalls;250059:
Gimme a minute so I can explain it with pictures.

Thank you so much.
Kueh wrote on 2010-12-16 22:01

It's kind of a big picture, sorry.

[Image: http://i57.photobucket.com/albums/g206/whyrainfalls/Triangles.png]

What the poop? Resize ftl. Hopefully you can still tell what I did even though you can't read it.

The words from top to bottom say,
In every Circle: (180-some amount)

Factor the unknown amounts, or the 180s depending on which way you want to look at it.

You know the sum of all the unknown amounts, the angles of a triangle, is 180.

Simplify.

(180-something)+(180-something else)+(180-another thing)=Answer
(180+180+180)-(All the somethings)=Answer

*All the somethings = 180

180+180+180-180 = 180+180 = 360
Akemii wrote on 2010-12-16 22:05

Did ju make that yourself?
Kueh wrote on 2010-12-16 22:08

Just now, yes.
Taycat wrote on 2010-12-16 22:09

You triforced wrong.
Time wrote on 2010-12-16 22:15

Quote from Whyrainfalls;250071:
It's kind of a big picture, sorry.

[Image: http://i57.photobucket.com/albums/g206/whyrainfalls/Triangles.png]

What the poop? Resize ftl. Hopefully you can still tell what I did even though you can't read it.

The words from top to bottom say,
In every Circle: (180-some amount)

Factor the unknown amounts, or the 180s depending on which way you want to look at it.

You know the sum of all the unknown amounts, the angles of a triangle, is 180.

Simplify.

(180-something)+(180-something else)+(180-another thing)=Answer
(180+180+180)-(All the somethings)=Answer

*All the somethings = 180

180+180+180-180 = 180+180 = 360

OMG THANK YOU, I GET IT NOW, THANK YOU SO MUCH!
Kueh wrote on 2010-12-16 22:17

Np Dog.

[Image: http://i57.photobucket.com/albums/g206/whyrainfalls/Naughtydoggie.png]

Np
Teaberry wrote on 2010-12-17 23:49

I was much lazier with my method, though Whyrainfalls did it correctly. Granted, I just glanced at the problem.

Disregarding the triangle in the very middle, you have a large triangle and 3 smaller triangles... more importantly you have the 3 unlabeled angles of the larger triangle (lets call them 7, 8, 9).

If you added up angles 1 thru 9, or the 3 small triangles, you'd get 540 (180 x 3). But since 7, 8, 9 is a triangle of its own you can infer that they equal 180 on their own.

Therefore angles 1 thru 6 must equal 360.

(That's my logic from a glance... I'm posting this in the case that it's incorrect, in which case the mistake can be corrected and not made again.)

[EDIT] After taking more than a glance I guess my logic is the same, just not as elegantly put.