If these lines are PARALLEL - what is the value of x? MUST know GEOMETRY!
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- เผยแพร่เมื่อ 20 ก.ย. 2024
- How to solve a geometry problem about parallel lines and transversal. Learn more math at TCMathAcademy.....
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When two parallel lines are intersected by a transversal, the corresponding angles are equal.
Therefore,
12X - 1 = 10X + 15
2X = 16
X= 8
I have to take a construction unions entry exam. I believe it's called the (act work keys)test. Does the website offer a course for that one or similar? Thanks. Love the content, it's a big help.
12x - 1 = 10x + 15, 12x = 10x + 16, 2x = 16, x = 8.
I'm sorry but I got confused now. You have 2 lines that leans differently, one with a factor 12 and one with a factor 10 and i seems to me that you calculated the intersection point between the lines. Indeed, if you plot the two lines [f(x) = 12x-1 and f(x) = 10x+15] you find they are not parallel and they do intersect at a x=8, f(x)=95. Can be easily done with Excel, or LibreOffice Calc.
Did I get something wrong here? If TH-cam would let me I'd upload the Excel file for you to see.
For a straight line (a linear function), y = ax + b, where a and b are constant, a denotes the leaning and b the offset value at x = 0.
(12x −1)° and (10x + 15)° are corresponding angles not functions for the slopes.
@@dazartingstall6680 My bad, sorry - only saw the expressions and took them for lines. Never heard about this angle properties of parallel lines, did a bit of research and found there are indeed applications where it's useful. Learning all the time as Benny Hill said...
got 8 just make the equations = thanks for the fun and I remembered 'transversal' from past decades.
Nice upload consistensy
Easy solution but John made it harder because the line intersections of drawing look to be closer to 90 degrees, whereas the answer is 8 degrees. This can throw your thinking off kilter.
We were asked to solve for x, which is 8°. The angles are multiples of x plus or minus a bit which comes out as 95°, so his diagram is pretty close to correct.
@@dazartingstall6680 I'm confused. Where did you get 95 degrees from? And how is that relevant? He says if the two white lines are parallel, then the 2 interior corresponding angles are =. (2 angles marked with blue chords). If those 2 angles are 8 degrees each, then the yellow line would be close to parallel to the 2 given parallel white lines. Instead, the drawing looks like the yellow line is perpendicular to the 2 lines. So the drawing is way different than verbal description.
@@terry_willis The two angles aren't 8°. x is 8. The angles are (12x −1)° and (10x + 15)°. Substituting 8 for x in both of those results in 95° for each.
@@dazartingstall6680 You are correct. I got hung up on X and missed the bigger picture. Thanks for explaining that to me.
8
10x + 15. Is it perpendicular to 12x -1
I.E. three lines and only one is carefully labeled.. I don't have necessary info to solve this problem.
Okay! So X has to equal 8 for the angles to be equal and the lines parallel but how do we know that X does actually equal 8?
We don't. The question asked is What would x have to be in order for the angles to be equal?
@@dazartingstall6680 My issue was that the quiz was "MUST know GEOMETRY" but it was an algebra quiz. They could have just said, "12X-1 = 10X +15. what is X?". For Geometry, they could have given the formulas for the angles and asked "If X = 8, are the lines parallel? and WHY?" Then it would have been Geometry.
@@thomasharding1838 You need to know that the two angles have to be equal if the lines are parallel in order to solve the problem.. That's geometry. To be honest, I don't really understand your objection. Much of geometry relies on algebra. It's why, as John points out, pupils learn basic algebra before geometry. The former provides the tools to deal with the latter.
@@dazartingstall6680 Oh, I realize that. Algebra, geometry and Physics were my go to subjects in school. My point is that it could have been more Geometry based if they had asked if the line are parallel if X = some value, rather than determining the value of X when the lines are defined as parallel. It is an Algebra question, not a Geometry one.
@@thomasharding1838 Your question tests the exact same knowledge of geometry as the one asked, no more and no less: that corresponding angles are equal only if the lines l and m are parallel. The only difference is that in your question we can see at a glance, just by substituting the given value of x, whether they are or aren't equal. It's still an algebraic problem: Do we have an equation or an inequality?
Too easy: 12x - 1 = 10x + 15 so x = 8 and the corner 95°
12x −1 = 10x +15
2x = 16
x = 8°
95°...
@@panlomito That's the angle, yes. But x = 8°.
@@dazartingstall6680 No, x = 8 and the angle is 95°... x is only a variable, not a corner with the given lines.
@@panlomito You're right. Thank you.
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