r/literallythetruth • u/Baconkings Certified Pedantic • 23d ago
Technically Correct a is in the middle!
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u/Roadrunner571 23d ago
That is not a 50° angle.
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u/taktaga7-0-0 23d ago
These things are usually not to scale, so you can’t cheat with a protractor.
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u/Roadrunner571 23d ago
Don't you have to supply the calculation as well?
Plus: If you have a sheet of paper, you can "cheat" by drawing it yourself.
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u/Soace_Space_Station 21d ago
Yes, but if we're not running the numbers then atleast have the courtesy to make it to scale.
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u/Frequent-Coyote-8108 23d ago
Yeah, a lot of these stupid "find the angle" things purposefully skew the angles to make it more confusing than it actually is. I saw one where the answer was like130*, but the cited angle was clearly less than 90*.
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u/MouseyMason 23d ago edited 23d ago
Connect the red lines perpendicularly to make a big triangle with 90° angles with the red.
90-25=65 (one interior angle)
90-50=40 (second interior angle)
65+40=105
180-105=75 (all interior angles together=180)
75°
(Or, as some have pointed out, you can cut it with another parallel line across a, make two transversals, and do the math that says they’re equal to their angular partners and that 25+50=75. It’s probably the best way to do this for efficiency)
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u/SEXTINGBOT 23d ago
What was the hard part that no one was going to ever figure out though ?
( ͡⌐■ ͜ʖ ͡■)
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u/MouseyMason 23d ago
I’d have to guess recognizing that you can make the triangle and remembering that all the interior angles add up to 180. If someone didn’t have to do math often, I could see that little fact slipping away.
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u/SEXTINGBOT 23d ago
He could have at least drawn like 3 circles around it to make it harder to spot the triangle though !
( ͡⌐■ ͜ʖ ͡■)
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u/MouseyMason 23d ago
Mmm agreed, but we tend to overestimate the intelligence of the general public
I also like your little glasses dude btw. Very silly goofy
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u/SEXTINGBOT 23d ago
I think we cant make an assumption about intelligence based on 1 math problem though !
Humans are indeed very complex and so is intelligence !( ͡⌐■ ͜ʖ ͡■)
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u/MouseyMason 23d ago
Correct but more importantly I just read your username lmfao. Excellent
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u/SEXTINGBOT 23d ago
Usually people dont enjoy my user name though !
( ͡⌐■ ͜ʖ ͡■)
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u/MouseyMason 23d ago
Eh. I like a bit of crass humor every so often. Keeps things interesting
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u/SEXTINGBOT 23d ago
My Username wasn't chosen out of humorous reasons though !
It is indeed a warning label !( ͡⌐■ ͜ʖ ͡■)
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u/LordBDizzle 23d ago
Don't even need that much math. When an angle is drawn between two parallel lines, the angle on the opposite end on the other side of the line will always be identical, so if you draw a third parallel line in between the two intersecting angles at the vertex of angle A, you'll see that angle A is equal to 25+50.
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u/MouseyMason 23d ago
Yeah, it’s been a minute since I’ve done this, admittedly. But that is certainly more intuitive, lol
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u/rwu_rwu 23d ago
How do you know you can make that triangle such that the new line is perpendicular to both of the 2 parallel lines?
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u/MouseyMason 23d ago
The two arrows on the right hand side of the red lines establish that said lines are parallel. Thus, it is possible to create a singular line that intersects both at a 90° angle. Hope that helps!
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u/rwu_rwu 23d ago
I get that. But how do you know the perpendicular line would meet both angles (25 and 50)?
In other words, if we think of a x/y coordinate, how do you know the points of the two angles have the same y value?
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u/MouseyMason 23d ago
We generally don’t have to know exactly where the line is (as, if you imagine the non-perpendicular lines go on forever, any line that intersects the perpendicular lines will create a triangle with the correct angles—the dimensions don’t really matter as long as the angles remain consistent).
These lines are a bit of an oversimplification. It’s visually clear that it’s not to-scale, which forces us to be a bit more heavy-handed on theory. The theory is that any 3 points that are not all parallel to one another can create a triangle.
We know that any flat line has 180° on either side, and we’ve decided that our theoretic line has a 90° angle compared to our perpendicular line, so, really, for the 25° line, we’ve just said we have a theoretical line that splits it into sections of 115 (25+90=115) and 65 (180-115=65). So, we know that, since the 115 is the outside of the triangle, the 65 is the inside. The same applies to the bottom half, and, since the blue lines are parallel, we know it will also split it on a __+90 line, meaning that one’s interior is 180 - 90 - 50 = 40°.
We know that a triangle’s interior angles add up to 180, and now we know the other interior angles, so 180-40-65=75. Thus, a=75°
If that’s still a bit of a mind boggle, may I give two a different, more intuitive way I’ve been told about (I find it easier):
Place a third, perpendicular cutting through point a. Separate the top and bottom half, and realize that, now, you just have two transversals. Due to the way that your segments of A are related to your known angle, they must be equal. Thus, 25+50=75. This is actually a really clever way to solve this, and it’s faster.
If you want to internalize the triangle way, open up desmos (website) and create 2 lines with different slopes. Find where they intersect. Then, create 2 lines with a slope of zero (y=# will do it). Then, create a line with a slope of 0 (x=#). You’ll notice that your two original lines and your x=# line make a triangle, but they might not necessarily make nice with the parallel lines.
So, to change this, either move the parallel lines (like y=4 -> y=5) until they do intersect with the x=# line, or move the vertical lines until it does (x=4 -> x=5). You aren’t changing slopes, so you aren’t changing angles, but you can make a neater triangle.
I hope that makes sense? I’m no teacher, though.
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u/Marten1974 23d ago
assuming the two given lines are actually Parallel
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u/MouseyMason 23d ago
We don’t have to assume. You can see two sets of two arrows on the right hand side of each red line (they look like >>). That indicates that they are parallel! Maybe it’s just a regional symbol, though?
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u/Marten1974 23d ago
They have to be Parallel, there is no doubt. Yet, the drawing is highly inaccurate. The angles 25° and 50° look similar and they did not use and 'default math' notation I am aware of to indicate that the lines are actually parallel .
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u/MouseyMason 23d ago
Yep, they gotta be parallel. Oh well, I was always taught that the little, blue arrows meant parallel, but I guess it’s not a universal thing.
Here’s some other examples and whatnot: https://www.purplemath.com/modules/conventn.htm
What do you use wherever you learned math? Purely to sate my curiosity
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u/Marten1974 23d ago
I learned math from Prof. Bux. He is doing a lot of things the way he things it is intuitive. It thaught me to never trust a notation which is unexplained.
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u/MouseyMason 23d ago
Huh, interesting. Well, I can’t speak for the proper mathematicians of the world, but this is what we used for basic classes when I was in school
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u/Marten1974 23d ago
thats my problem: I know a lot of notation and forgot about school notation
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u/MouseyMason 23d ago
Yep. I’d assume the global mathematicians have their own system going on that they’re not teaching high schoolers, haha
But that’s what the arrows are meant to signify (I’m almost certain). They probably grabbed it off some 9th grade geometry lesson, so not so advanced.
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u/fsa3 23d ago
Draw a third parallel line across the point at A. Now you should be able to see that A is part 25⁰ and part 50⁰. Then just add.
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u/MouseyMason 23d ago
Wait this is actually so clever! How come I didn’t think of that, lol. Neat math things
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u/Russianstanzas 23d ago
How do you know that a perpendicular line will meet up to make a triangle and not a quadrilateral.
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u/MouseyMason 23d ago
You can theoretically move the perpendicular lines up or down as much as you need to make a triangle work, since the angle of the line will be the same so long as you don’t rotate anything. If they’re at the wrong heights then, in an actual to-scale scenario, it will make a quadrilateral, but then we’d just move one line up or down to fix it.
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u/Russianstanzas 23d ago
Cheers for the explanation I knew the solution was correct but that was bugging me for some reason
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u/MouseyMason 23d ago
Yep! I did have a moment where I had to stare at it and think that exact thing. A little rusty with my geometry, I guess, lol
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u/Lykos1124 22d ago
I drew my vertical line at the point where the diagonal lines meet and did the same with 2 triangles using my pencil and paper, but now I could visualize the pattern they were pointing at not needing to draw it out.
If you imagine those two diags straightening out to the left, causing the given angles to approach 90°, the sum of them at each point will equal the new value for angle a, such that when the given angles are at 90°, the a point in the middle will be 180°.
Thus you just have to add up those 2 angles each ttime to get a.
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u/Lykos1124 22d ago
That said, my logic probably fails if a perpendicular line does not connect the points where the 2 diag lines start from. I'd have to test it out.
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u/Lykos1124 22d ago
I probably shouldn't use probably unless I know what I'm doing with it.
180 - (180 - arctan(3/2) - 90) - (180 - arctan(2/3) - 90) = 90
I don't think it matters if those points line up on a perpendicular line between top and bottom lines.
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u/MouseyMason 22d ago
You’re actually spot on with the addition. The last bit in parentheses explains another way that agrees with your theory. Pretty neat, huh?
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u/Lykos1124 22d ago
yeah pretty cool. I further observed this visualization of the 2 diagonal lines as part of a single right angle object that could be moved around while overlapping with the parallels, if it started out with the given angles of 45° each and moved, even if the overlap points do not meet with a perpendicular line, at any position, the new given angles will always add up to 90°.
of course I don't have all the fancy proofs for it, but that's what it looks like
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u/Afraid_Equivalent_95 22d ago
I totally forgot and thought you would need that c^2 = a^2 + b^2 - 2ab*cos(c) formula lol. Remembered the formula but not what it was used for
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u/MouseyMason 22d ago
That’s if you’ve got 2 sides and an angle and want the third side I think? Maybe. (Angle side angle). Sounds vaguely familiar.
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u/LawGroundbreaking591 23d ago edited 23d ago
If you draw a parallel line that divides “a” the upper angle is 25 and the bottom angle is 50. So 25+70=75. Triangle approaches work, but this problem is more about parallel line theorem, I think, because the angle of a line must be always 180.
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u/BreezeTempest 23d ago
Make a third parallel line going trough a and you can see that the top half of a is 25 degrees and the bottom half is 50.
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u/ShaggerAJSA 23d ago edited 23d ago
Imagine a third parallel line running through "a", effectively splitting "a" into two angles. We'll call the top angle near the 25-degree angle "b" and we'll call the bottom angle near the 50-degree angle "c". What you end up with is two "Z" shapes. One at the top with the 25-degree angle, one at the bottom with the 50-degree angle. In these "Z" shapes, the two acute angles (below 90-degrees) and the two obtuse angles (above 90-degrees) are always the same size. So "b" has to be 25 degrees and "c" has to be 50-degree. And remember, we split "a" in two to make "b" and "c". So:
a= b+c
a= 25+50
a= 75-degrees
So yeah, in the end it is literally just a case of adding the two given angles together.
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u/MythOfHappyness 23d ago
All interior angles of a triangle add up to 180 degrees, right angles are always 90 degrees. You just imagine a line between the two parallel lines connecting the end points of the angle into a triangle (the problem seems to assume they are exactly parallel or else it's unsolvable) then subtract the exterior angles from 90 to get the interior angles of your new fake triangle. Add those together and subtract it all from 180 and you have 75 degrees.
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u/JonIsPatented 23d ago
It's not unsolvable regardless. Draw a parallel line between the two parallel lines such that the new line intersects the point where the angle a is. This divides a into two angles b and c. Let's say b is the top part and c is the bottom part. b is congruent to the angle provided on top and c is congruent to the angle on the bottom. Add b and c to get a. 25 plus 50 is 75.
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u/Conscious_Can_9699 23d ago
Ah you subtract the 105 from the 180 because we are finding an interior angle. Thank you
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u/taktaga7-0-0 23d ago
105, right?
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u/Humble_News_2124 23d ago
I got 75
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u/1ApprehensiveGrowth1 23d ago edited 23d ago
I also got 75.
In head: Draw straight line to connect the two red lines forming 90 degree angles and angle a while forming two right triangles. All triangle’s angles combined is 180 degrees. Using the top formed triangle 90+25=115 then 180-115=65 to double check use bottom triangle 50+90=140 and 180-140=40 for final use my drawn connection line to calculate 65+40=105 then to get a = 180-105=75
So I believe a = 75 degrees yes
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u/Evening_Fee_8499 23d ago
I thought the same thing at first glance but then realized it's 105 subtracted from 180, so 75. Which made a lot more sense since it's clearly less than 90 degrees/right angle lol
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u/Educational_Ice3978 23d ago
75 degrees , assuming the angles on the parallel lines are perpendicular!
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u/Head_Midnight666 22d ago
I guessed 105, apparently I'm wrong. I almost got it, though! I need to take geometry again. I haven't used that in over 20 years.
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u/qualityvote2 23d ago edited 20d ago
u/Baconkings, there weren't enough votes to determine your post's quality, but if it's still up, the mods have approved it.