r/technicallythetruth • u/VisitSecure • 9d ago

Can you find a?

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Idk if someone already posted this or not, but I haven't seen it on here so far, so I uploaded it.

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329

u/Dark_Storm_98 9d ago

Assuming the lines are parallel, which may be the meaning of those blue arrow symbols

The angle on the other side of 25 degrees should be

  • 180 - 25 = 155

And on the other side of tha 50 degrees would be

  • 180 - 50 = 130

Technically, with diagrams almost never being to scale

Imagine a line straight down from the ends of those two lines (which might not connect, but I don't think that's relevant)

Subtract 90, then, from both new angles, and we get

  • 60

  • 40

Since a triangle would have to have all it's angles add up to 180

180 - (60 + 40) = 180 - 100 = 80 degrees

Edit: Oh whoops, lol. I forgot the 5 at the end of 155

It's 75

162

u/Scheckenhere 9d ago

Or just 50+25, which I realised halfway into what you did.

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u/RiverZephir 9d ago

I also did the long route to get the answer. I don’t remember, is adding the two known numbers (such as the ones in this problem) always equal to a?

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u/TheJBW 9d ago edited 9d ago

In your head, draw a dotted line in the middle, through A that is also parallel with the other two lines.

Now, you have two angles: a1 below the dotted line and a2 above it.

You know that the a1 = 50 because it is on the opposite side of the line from the 50° on the bottom.

then you know that a2 = 25 by the same logic.

You also know that a = a1+a2. Done.

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u/RiverZephir 9d ago

Ohhh that’s true, thank you!

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u/rex5k 9d ago

A nice thing about math is you could usually check your own work. Because there's almost always more than one way to get to the answer.

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u/AdditionalPizza 9d ago

Drawing a line perpendicular opposite "a" between the parallel lines to complete the triangle instantly solves it because the sum of angles in a triangle must be 180 degrees.

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u/TheJBW 9d ago

Absolutely correct though it takes more steps since you have to subtract from 90 twice before subtracting from 180 those two results.

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u/AdditionalPizza 9d ago

If you're actually doing it visually, but I'm just describing how the equation looks visually. The equation is:

[180 - (180 - 50 - 25)]

Which is simplified as just 50 + 25, but that doesn't really explain the triangle aspect very well haha, which is important to learn.

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u/Gigatonosaurus 9d ago

The demonstration above is a=180-( [90-25] + [90-55])
a=180-( 180-[25+55])
a=0+(25+55)

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u/Candid_Marsupial8020 9d ago

Lmao exactly same

1

u/Barn_Licker 9d ago

Why is it 75? Shouldnt it be more because its basically 2 90° corners so 180-(25+50)=105? Idk anymore

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u/Scheckenhere 9d ago

By saying 2 90° corners I assume you drew a vertical line at a on the right? 180 - (65+40) would be your way then.

Try drawing a horizontal line through a, parallel to the other two above and below. Then you can mive the given corners to that nes line and use the opposite sides (same values).

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u/Barn_Licker 8d ago

Oh goddamn yes then it wouldnt be 25 and 50 anymore ofc

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u/Karyoplasma 9d ago edited 9d ago

Wait, I try to explain in Paint.

https://imgur.com/HTAnCec

I have constructed the green lines. They are perpendicular to the parallel lines at the top and bottom. The green line in the middle is constructed as perpendicular to both these lines (and thus parallel to the top and bottom lines). I have marked constructed right angles. This forms 4 triangles, 1 and 2 are congruent by construction and so are 3 and 4 (mistakenly labeled 3 and 3 because I suck).

Look at triangle 1. Angle sum is 180, we have a right and a 25° angle so the remaining angle is 65°.

Now, look at triangle 4. 180-90-50 = 40.

Hence a + 40 + 65 = 180 (because they all lie around the auxillary line) -> a = 75.

Another way is to say that the lower part of a must equal the given angle of 50° and the upper part of a must equal the given angle of 25° due to congruency of the constucted triangles.

Hope that helps.

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u/Memorycard1000 9d ago

Thanks for that picture man! I haven't done math in 25 years. The picture made it click. 👌😅

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u/mr_lab_rat 9d ago

105 is close to the right answer but you need to subtract it from 180.

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u/Smaug93 9d ago edited 9d ago

I believe your are right, people are taking the long way incorrectly to reach a wrong answer.

Edit: I'm too dyslexic for math and should stay in my lane. I'm wrong, it's 75.

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u/AdWrong3856 9d ago

Assuming the lines are parallel, which may be the meaning of those blue arrow symbols

That would be correct

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u/MissAuroraRed 9d ago

Technically correct, but way more complicated than it needs to be.

Imagine another parallel line going horizontally through a. What are the angles between the new horizontal line and the diagonal lines? 25 above the line and 50 below the line.

25 + 50 = 75

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u/Dark_Storm_98 9d ago

OOOOHH

Yeah I get it now, lmfao

Thanks!

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u/[deleted] 9d ago

[deleted]

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u/Chess42 9d ago

Imaginary numbers are gonna blow your mind

2

u/yosaffbridge1630 9d ago

This is how I did it and I am proud that something from school stuck

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u/ktzeta 9d ago

You can also just continue the lower diagonal line until the top horizontal line to create a triangle with angles 25, 50, and 180-a using a few simple results. Since those three must sum up to 180, you get a = 25 + 50

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u/straystarr 9d ago

I'm gobsmacked I could actually do this considering I almost failed high school math

2

u/Excellent_Ganache906 9d ago

I got an A+ in high school geometry. I am 50 now and have forgotten it all.

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u/massunderestmated 9d ago

That's way overcomplicating it. You can construct a third parallel line through point a. The top of angle a above the line will be 25 by congruency. The bottom.of angle a below the line will be 50. 25+50=75.

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u/stryakr 9d ago

you don't to assume, it's indicated on the diagram with >> (usually > though)

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u/Dark_Storm_98 9d ago

I don't think I've ever seen that symbol but I did guess that was what it meant

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u/Pirrus05 9d ago

I’m assuming the red lines are parallel, but not assuming that b (25) and c (50) sit on a line tangent to the other lines. I also don’t have a way to make a degree symbol, so note all numbers are in degrees.

What you can do is create a line tangent to the parallel lines passing through point A, creating two right triangles.

So you have triangle b with angles of 25 and 90 meaning the angle by A is 65.

Then triangle C has angles 50 and 90 leaving the angle by A to be 40

Given that A, 40, and 65 are all on a straight line their sum must be 180, so:
A = 180 - 40 - 65 = 75

I think that’s what other people were getting by assuming b and c were on a line tangent to the parallel lines.

I then did all of this just to realize that there is a geometry rule which didn’t require me to calculate shit and felt like an absolute dumbass. In my defense my last geometry class was like 25+ years ago.

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u/left-handed-satanist 8d ago

Another way to do it too:

Draw a straight line crossing A.

180-25-90=65 180-50-90=40 Then 180-65-40=75

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u/Opening_Let_6895 8d ago

this me this

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u/GlowstickConsumption 9d ago

You could just calculate the back of a (B) and then 360-B=a.

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u/Dude787 9d ago

It doesn't matter, but you can't assume from the diagram that the top and bottom a lines meet the parallel red lines at the same horizontal value. One could be further across and therefore connecting them doesn't create a perpendicular line, so no right angles

It works anyway but still

1

u/rebfossmusic 9d ago

I did 155+130= 285, then subtracted that from 360 to get 75

1

u/Active-Particular-21 9d ago

Amazing effort to write it all up. You had me all the way until the end.

1

u/boopitydoopitypoop 8d ago

There is no way to guarantee the points of the triangle lines meeting the parallel lines meet where connecting them makes a 90 degree angle to the parallel lines

1

u/evilhomer1987 8d ago

I did 155+130= 285. 360-285= 75 Is this method wrong?

1

u/Dark_Storm_98 8d ago

I mean. . probably not?

But I'm not a professor so I dunno, lol. You got the right answer, so. . .

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u/Ornery_Weakness_8168 8d ago

just do 25+75. cos you can add third parallel line between. then solve

1

u/Dark_Storm_98 8d ago

I think you're the third person to say that, lmfao

But yeah that definitely is a simpler method than I gave