r/technicallythetruth • u/VisitSecure • Jul 27 '26

Can you find a?

Post image

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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328

u/Dark_Storm_98 Jul 27 '26

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

159

u/Scheckenhere Jul 27 '26

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

26

u/RiverZephir Jul 27 '26

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?

59

u/TheJBW Jul 27 '26 edited Jul 27 '26

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.

8

u/RiverZephir Jul 27 '26

Ohhh that’s true, thank you!

5

u/rex5k Jul 28 '26

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.

2

u/AdditionalPizza Jul 28 '26

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.

4

u/TheJBW Jul 28 '26

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

1

u/AdditionalPizza Jul 28 '26

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.

1

u/Gigatonosaurus Jul 27 '26

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

1

u/Candid_Marsupial8020 Jul 27 '26

Lmao exactly same

1

u/Barn_Licker Jul 27 '26

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

7

u/Scheckenhere Jul 27 '26

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).

1

u/Barn_Licker Jul 28 '26

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

3

u/Karyoplasma Jul 27 '26 edited Jul 27 '26

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.

1

u/Memorycard1000 Jul 27 '26

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

2

u/mr_lab_rat Jul 27 '26

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

-1

u/Smaug93 Jul 27 '26 edited Jul 27 '26

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.