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PLEASE HELP!!!!! (drawing attached) "For the two intersecting lines in the drawing, which of the following must be true?" (A) a>c (B) a = 2b (C) a+60 = b+c Please explain why the answer to this questions is: "Only B and C are true." Thanks! =)

Mathematics
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|dw:1338591680453:dw|
Well, if we use the idea that a line will always create an angle of 180 degrees, we can see: a + 60 = 180, a + b = 180, b + c = 180, and c + 60 = 180
Okay, I do get that, but why would a=2b ?

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Other answers:

Well, let's solve for a: a + 60 = 180 subtract 60 from both sides: a = 120 Then, if we solve for b in a + b = 180, using a = 120: 120 + b = 180 b = 60 If we double b, it'll be the same as a: 2b = a
OH, I see! Okay - that makes sense. Well - thank you so much for taking your time to explain it! I really do appreciate it! :)
You're welcome! I'm glad to help. :)
Thanks - you're really good at it! :)
Hmm, thanks. :P Geometry is my favorite type of Math so far. :D
Ha, ha - I know what you mean! I enjoy it the most (well . . I also enjoy Algebra1, as well), too. It's much more creative!
Yeah. Some of my favorite problems come from Geometry. :D Like one about a length of cable to attach a cylinder to a flatbed: truck |dw:1338593807626:dw| Having to find the length of the entire cable given only that radius. (This was a problem I encountered on OS :D)
Oh, and that the angle in the corner was 60 degrees. lol |dw:1338594186655:dw|
Boy! - that certainly looks a little tricky! Did you solve it?
Oh, ha, ha - yes, the angles does help! :)
*angle
Yeah, it essentially breaks down into a 30-60-90 triangle and the arclength of the top: |dw:1338594286628:dw| So the actual length just comes down to \(2 \pi + 6\sqrt{3}\) That problem is just so interesting, involving all these different important concepts. :D
Wow! I don't think that I've seen too many Geometry problems with so many concepts involved! You are right, though - it does involve quite a few different concepts! :) Good for you for figuring out the answer! I'm most impressed! Keep up the good work (and the good brains:)!
From your level of math ability, are you a college math student? You seem to be very good at what you do!
Thanks. :) Yeah, I'm gonna go back to reading a Geometry book in a sec. The book goes over a lot of stuff I didn't get to see in class. High School, just passed 10th; I just finished Geometry / Algebra II.
Wow! That's incredible! I'm assuming you just passed 10th grade because of the school year ending? In 5 days I, too, finish Algebra 2 and I'll finish 11th grade!! I can't wait! Are you reading a Geometry book for fun, or are you taking some summer classes?
Yeah, it's the end of the school year. Nice! :D This one is for fun. I just started on it, too. It starts out proving an extended law of sines, which was quite a surprise to me. lol
Ha, ha - yes, that is kind of surprising! So, you must be planning on going into some brainy math field in college?
Yeah, that'd be possible. I think at this point, I wouldn't even need to listen in Math class for the next few years, since I've studied up to Calculus II and a little of Calculus III / Linear Algebra. :P
Woah - you're blowing me away! :) I think the most that I would ever want to go up to is Trigonometry and Pre-Cal. - I'll leave the rest to all of you brainy people out there. ;) I was surprised that Algebra 2 wasn't as bad as everyone says it is. I thought it'd be a lot worse. That was nice, though.
It's good that Algebra II wasn't so bad for you. At least, from what I've seen... I was surprised by my Algebra II class and how not-ready the other students were. They always wanted to kick me out of class because the teacher wouldn't curve the scores when I got 98-100% on every test. lol
Ha, ha - that's funny. :) You definitely have a natural gift for math! I ended up having to repeat 4th grade because math was so difficult for me to understand (ha, ha - can you imagine me - a then little 4th-grader struggling with multiplication and division! - and I made it all the way to Algebra 2!) :) I'm glad I'm better at it now, though. I would never have had a chance of getting into college, with the scores I had, back then! Where you're so good with math, were you/are you homeschooled? or do you just understand math really well?
Interestingly, I don't recall myself being that great at all the grade school math. I didn't even get to go to Algebra I early when I had the chance in 8th grade. It was sometime after I learned I had to go to Pre-Algebra (which was sorta annoying I guess) that I just started studying Math myself, usually just Googling different things like basic sine/cosine stuff and imaginary numbers. As I went on with that, I soon picked up this strange interest in the subject. Eventually I got into Calculus / trying to figure out limits, and once I overstepped limits, I think everything just started making sense to me. D:
Cool! - I wish my story was like that. I do understand what you mean about it making sense, after awhile. That's what I noticed happened with me - It's like something just clicked.
If you're not busy, right now, I actually am stuck on another Geometry problem (it's a triangle within a triangle). Do you want to have a go at it and see if you can figure it out?
Sure. :) Limits were probably the absolute hardest thing ever to actually understand for me, it took all year to figure it out.. lol
Ha, ha - I can't imagine! Okay, here goes . . . . .
In triangle PQR (shown in the drawing below), w = (A) 50 (B) 55 (C) 60 (D) 65 (E) 75 Here's the triangle: |dw:1338596635921:dw|
Here, I see enough information to use the property that the sum of interior angles in an n-gon is \(180(n-2)\) |dw:1338596846040:dw| The sum of that big angle and 140 is 360 (circles are 360 degrees) t + 140 = 360 t = 220 Then, we just have to use: w + 35 + 40 + 220 = 180(4-2) = 360
Ah - okay, I see! So, when you solve, you would get: 65 Is that correct?
Yep! :)
I forgot about using the angle outside of the 140 degree angle - that part always trips me up! Thank you, again, for your outstanding help! In case you're wondering why I have so many questions, I'm going to be taking the SAT tomorrow, so I'm practicing SAT test questions, right now. OpenStudy and you have been so helpful! I love having this site, instead of having to get a tutor! :)
Ahh, nice. Good luck! Yes, I love this site also. I've met some very cool and smart people here. :D
Thanks! I'll need it!!! Yes, I agree - some of the people on here are really good (you included ;)!
You're welcome. ) and thanks. I've still got a lot to learn in Math though, and this site is helping me to see what I know and don't know. :P
I know! - math is just never-ending (ha, ha - sounds like a good title - "The Never Ending Story" :). Well, if you ever need my help with writing (grammar, etc.) or any other subject besides math (I don't think I'm quite up to your level, with math, yet:), I'd be happy to help! I'm pretty good with the more creative side of things, if you know what I mean.
Hmm, that could be a possibility, but next year. :P Thanks!
Sounds good.
Well, I'll see you later! I have to get back to this Geometry book. Bye, and good luck once again!
Sounds good! You, too! Thanks so much! =)

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