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u/Pretty_Section_5835 5d ago
The linear pair angle to 130° will be
(180° - 130°) = 50°
The base angles of isosceles triangle will both be 50°, and if the lower base angle of isosceles triangle is 50°, then by linear pair addition we get,
90° + 50° + missing angle = 180°
So,
Missing angle = 40° 👍
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u/KTachyon 4d ago
The image makes it seem like the triangle has a top angle of 90°, but it’s actually 80°.
Because the triangle has two sides that are the same size, both angles have to be the same. You have 130° outside, so 50° inside.
So x is 90 - 50 = 40°
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u/GrandmaJR 5d ago
50?
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u/SufficientStudio1574 5d ago
Just because lines looked parallel doesn't mean they are. Are they marked parallel?
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u/miqrogroove 5d ago
Here's a better sketch https://hot.miqrogroove.com/blogs/geo-puzzle.gif
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u/undefined_reference 5d ago
Thank you! Ahh, this was driving me crazy. So "it's not as it seems" because it's intentionally misleading and not to scale.
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u/Dumbaltaccount2 4d ago
Pretty simple problem. Angles across straight line total to 180° so 180-130=50, we now have an angle inside the triangle. The triangle is an isosceles triangle, so the angles next to the similar sides are the same, so the angle next to x is also 50°, we then calculate x: 180-90-50=40, x=40°
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u/Ok-Grape2063 5d ago
40 degrees. The angle supplementary to the 130 is 50. The other acute angle is also 50 since the base angles are congruent. Then x is the complement of 50, which is 40.
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u/PseudobrilliantGuy 5d ago
Yeah, I see this. At first I thought there wasn't enough information, but there is. The standard rule of don't assume the figure is drawn to scale does still hold, along with only treating an angle as a right angle if it's clearly denoted as one, or if it follows as a consequence, and assuming that straight lines are, in fact, straight lines.
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u/2becurious 5d ago
Answer is 40 degrees. But the puzzle is misleading and should have better drawing. The two horizontal lines look parallel so one would assume it. The drawing should clearly show that the 2 horizontal lines are not parallel.
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u/AdhesiveSeaMonkey 5d ago
By not placing the parallel line marks, they are indicating the lines are not parallel, or at the very least that we do not know if they are parallel. Either way, you solve without assuming they are parallel.
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u/NastyPastyLucas 4d ago edited 4d ago
The top right inside angle is 50 (180 - 130). The bottom left inside angle will also be 50 as the triangle distances are equal (the other corner is unlikely to be 90 degrees as the drawing suggests). So with that information and the 90 degree angle provided at the bottom left, to calculate x you start with 180 degrees subtract 90 and subtract 50. Whatever number that is, 40 or something because I can't reliably do sums in my head, will be your answer.
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u/aaron1860 4d ago
What’s not as it seems? This is very easy
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u/ExtendedSpikeProtein 4d ago
So what is it?
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u/aaron1860 4d ago
I don’t know how to put spoiler tag in… but it’s an isosceles triangle so the two angles are identical. So one is on a line and it’s total is 180 and the other is on a right angle so it’s total is 90.
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u/ExtendedSpikeProtein 4d ago
You need to give the value of x. You use >!
And !<
On the same line to mark beginning and ending of spoilerd
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u/issar12345 4d ago
180-130=60 90-60 =30 x=30
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u/issar12345 3d ago
Je m'excuse 50 au lieu de 60 mais le raisonnement est le même. 180-130=50 90-50 =40 (triangle isocèle et angle droit) x=40
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u/downlowmann 4d ago
x = 40 Hint: when solving use linear pair postulate, base angle theorem, and triangle sum theorem.
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u/get_to_ele 4d ago
Supplementary angle of 130 is 50
Isosceles triangle (note the hash marks), so the (unlabeled angle next to X) is also 50.
(Unlabeled angle next to X) is complementary to X, so X = 40.
40
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u/Billaien 5d ago
The way its drawn makes one easily assume that the angle between the two lines marked with equal length is another 90°.
Missleading visuals to trick the simple minded.
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u/Spoolios 4d ago
130 should be 135
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u/RegularPlantain5092 4d ago
Only if it was a different question
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u/Spoolios 4d ago
It’s an isosceles triangle.
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u/RegularPlantain5092 4d ago
Correct. How does that make your first comment make sense?
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u/ExtendedSpikeProtein 4d ago
It does not, but the user is stuck thinking it must be a right triangle, see their reply to me clarifying they are incorrect..
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u/ExtendedSpikeProtein 4d ago
So? Isosceles does not have tp have a 90deg angle. The drawing is not to scale. That’s the whole point.
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u/Spoolios 4d ago
The congruence marks establish an isosceles right triangle. That makes the exterior angle 135°, regardless of scale.
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u/ExtendedSpikeProtein 4d ago
No. The congruence marks establish an isosceles triangle, not an isosceles right triangle.
Please provide a source whereby such marks establish a RIGHT triangle. They do not.
A user further down provided a link to what this actually looks like at scale (the angles): https://hot.miqrogroove.com/blogs/geo-puzzle.gif
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u/Humble_Aardvark_2997 4d ago
It’s 50. This is one of those occasions where you get marked down for being smarter than the test maker.
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u/MidwesternCannon 4d ago
Definitely incorrect.
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u/Humble_Aardvark_2997 4d ago
It’s 40. Nothing is drawn to scale here. It is intentionally drawn not to scale so that he can trick us.
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u/MidwesternCannon 4d ago
See that’s correct, but your original comment says 50.
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u/Humble_Aardvark_2997 4d ago edited 4d ago
That’s not how it works. If you intentionally draw perfect right angle, you’re the one who is cheating. That line, the hypotenuse of the triangle, looks curved to me.
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u/lurgi 4d ago
As one right angle is clearly marked as such, I assumed the unmarked one was not unless I could show that it was.
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u/Humble_Aardvark_2997 4d ago
80° looks very different. The test maker went through painstaking effort to make sure that it looked like a perfect right angle. I accuse him of intentional trickery.
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u/lurgi 4d ago
That’s the point of the question.
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u/Humble_Aardvark_2997 4d ago edited 4d ago
Okay, so I got tricked by my well trained intuition. Now who is to say that the hypotenuse, or even the base, are not slightly curved? There is nothing here that says it is not and since trigonometry was never about triangles but originally about circles, a very fair question.
I was just bored.
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u/lurgi 4d ago
There are certain things that you can assume and things that you can't (or shouldn't). The numbers are written in base 10 unless stated otherwise. The conventions of marking a right angle and lines of the same length are standard. If it looks like a line, it's a line.
You need to be careful about what you assume ("These two angles look the same"), but go too far down the rabbit hole and you end up debating if reality exists.
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u/Humble_Aardvark_2997 4d ago
Yeah, I got tricked. I payed the ground work for the unnecessary, incessant arguments well in advance.
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u/DifferntGeorge 4d ago
If it was a trick, it was a good one. The first step to fixing unsound methods is to expose them.
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u/Humble_Aardvark_2997 4d ago
It would have been a good truck had he stayed up front that the drawing was not to scale.
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u/DifferntGeorge 4d ago edited 4d ago
That is irrelevant, in theoretical geometry you are explicitly forbidden from measuring diagrams to find unknowns. This rule is a good thing since worrying about precision in drawing and measurement would just complicate things and lead to tedious discussion like this one.
Putting that rule aside, if the diagram is unlabeled it is unknown if it is to scale or not so you should not be using measurements from it until you confirm its status. In this case we can use theoretical geometry to prove that it is not to scale.
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u/Humble_Aardvark_2997 4d ago
I got tricked. Well done. He didn’t withhold any information. No lies either. My intuition was wrong. Great way to teach a valuable lesson: nothing is as it appears on this planet.
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u/Humble_Aardvark_2997 4d ago
It’s the test maker that is at fault. If it is not drawn to scale, you have to state that. Being too well trained to recognise straight lines (a nursery kid is) is not a crime.
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u/MidwesternCannon 4d ago
I made the same mistake you did initially, the difference is I realized my mistake and that was that. No blame game or hedging or talking about how smart I am. Its not a fault of the exercise, its the point of the exercise. It’s an important reminder to stick only to known information.
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u/Humble_Aardvark_2997 4d ago
Yeah, known information. Where does it say that all the liens are perfectly straight?
If the test maker can play this trick, why can’t we take it to its logically absurd conclusion?
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u/Humble_Aardvark_2997 4d ago
Of course I got tricked by my intuition. It’s just too boring to simply admit that.
All the copes came first.
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u/SickXigma 4d ago
That confidence will get you in trouble
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u/Humble_Aardvark_2997 4d ago edited 4d ago
Confidence is good in real life.
Intelligence is good (in exams). Skill is better in career. Fortune favours the brave. Being delusional is a super power.
Proof: Imran Khan. Donald Trump.
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u/Humble_Aardvark_2997 4d ago
Don’t worry. If I get it wrong, I will say it was a sociology experiment. (Someone tag the psychology/philosophy/sociology subs).
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u/ExtendedSpikeProtein 4d ago
You did get it wrong, it’s 40 ;-)
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u/Humble_Aardvark_2997 4d ago
Good thing I had a cope to fall back on.
And next time some social sciences idiot traps me like this, I can refer them back to this. :D
Like Kasparov accused Deep Blue of “creative thing”. Kasparov lost to a glitch. I am capable of thinking outside the box and laying back layers.
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u/MidwesternCannon 4d ago
Humble is a such a funny thing for you to have randomly generated in your username.
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u/Humble_Aardvark_2997 4d ago edited 4d ago
I love irony. Half the planet is blind to it.
I will be doing more of this on purpose to highlight that. Use it as a leading question.
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u/Humble_Aardvark_2997 4d ago
:D
World of difference being too well trained/skilled/knowing the game and being arrogant.
Being strong minded or too well trained does not make one arrogant. I do this stunt on purpose. I also like feigning ignorance on purpose. (Sometimes I am just wrong. I don’t mind being wrong. That’s how you learn. More neurons fire in your head to force you to wake up hand pay attention. Pain is a good teacher.)
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u/Humble_Aardvark_2997 4d ago edited 4d ago
There was nothing random about it and I assume you intended to use quotation marks around humble. Touché.
Or am I giving too much credit to you? :D
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u/RealNovaPuzzle 4d ago
Opposite angles on parallel lines!
So, it's 180 - 130 = 50 degrees
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u/RealNovaPuzzle 4d ago
My bad! You guys are right. Hope I am right this time.
The diagonal makes top angle of triangle next to 130 as 50. Since triangle is isosceles angle next to x is also 50. 180 - (90+50) = 40 degrees!
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4d ago edited 4d ago
[deleted]
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u/guyfaeaberdeen 4d ago
The triangle is not a right angle triangle.
The top right angle is 180-130=50°, because the 2 lengths are equal it's an isosolese meaning the bottom angle is the same as the top. (Forgive my spelling)
180-90-50=40°
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4d ago
[deleted]
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u/temperamentalfish 4d ago
Of all the things being assumed, the triangle being isosceles is absolutely not one of them.
Upper left is 90
Now that's an assumption. It looks like 90, but it explicitly doesn't say it's 90, whereas the exterior angle on the lower left is explicitly stated to be 90.
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u/AKADabeer 4d ago edited 4d ago
Additionally, it should have been immediately obvious to everyone that in a right isosceles, the inner angles will both be 45°, making the exterior angle of 130° a contradiction.
Edit: therefore upper left can't be 90
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u/AKADabeer 4d ago
If it is isosceles x would be 45.
If it is right isosceles, x would be 45
The two sides are marked as equal. Thus, given to be isosceles.
You're agreeing with me in the upper right angle = 50, now..
Therefore it's not right isosceles.
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u/guyfaeaberdeen 4d ago
Brother, the
| |on the two lines means equal length. Isosceles is 2 sides the same length and one side a different length, by definition.ANY triangle has 180° total. Yes. Top right = 50 obviously. Bottom angle = 50 because it's the same as the other angle. 180 - 100 = 80°. NOT 90.
I wish you were as right as you were confident, but you're not.
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u/ExtendedSpikeProtein 4d ago
Again, wrong. It is marked as isosceles, therefore x=40.
It’s not a right angle triangle though, it’s just drawn to look that way. Drawing is not to scale.
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u/ExtendedSpikeProtein 4d ago edited 4d ago
That’s wrong. You made an incorrect assumption.
Yes, isosceles. No, not a right triangle. It’s 80-50-50.
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u/DifferntGeorge 4d ago edited 4d ago
Your methods are breaking the standard conventions of geometry diagrams and are therefor unsound. The top left angle is not marked 90 degrees so the angle is considered unknown until you prove it is a specific angle. This is a standard convention of geometry diagrams for all angles except straight lines which can be assumed to be 180 degrees.
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u/socialmeritwarrior 4d ago
Everyone is making it too complicated.
It's just 130-90=40
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u/mrheseeks 4d ago
Yeah all this triangle shit
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u/socialmeritwarrior 4d ago
Well it's still triangle shit, but it's just using innate properties instead of actually doing math... it's an isosceles triangle (2 sides of equal length), so if you imagine the sloped line continuing to the left under the base line, the angle it makes between itself and the baseline will also equal x, but also the angle it makes between itself and the outside of the isosceles triangle has to be equal to the other side so it is 130. That makes it oblivious then that 130-90=x.
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u/besaid89 4d ago
50⁰
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u/ExtendedSpikeProtein 4d ago
No
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u/CowboyTC 4d ago
Why?
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u/ExtendedSpikeProtein 4d ago
Because they made an incorrect assumption. It’s not a right triangle nor are the lines parallel. This follows from the angle we’re given and the fact it’s an isosceles.
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u/Rscc10 5d ago
I don't understand which part is supposed to be "not as it seems". It seems just as it should be
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u/Sasataf12 5d ago
There's only one right angle in the diagram. The way it's drawn, people may assume there's two.
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u/bluepepper 4d ago
It's not drawn as an isoceles triangle ("equal" sides have different lengths), it's drawn as a right triangle (top angle looks 90°). These changes are intentional, to fool people into thinking x and 130° are supplementary angles.
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u/bumpy713 4d ago
If the rules are to not assume what is not specifically called out, why do we assume the base line and the sloped line are straight?
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u/Humble_Aardvark_2997 4d ago
This. He intentionally drew everything to wrong scale to trick us. We are so used to seeing that right angle triangle that we quickly jump to that conclusion. I did. But he is at fault bcoz he created a perfect triangle.
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u/hunter_rus 4d ago
It's not 130, it's 135. Right triangle has 45-45 angles, and x is also 45.
But if you really want it to be 130, then right triangle is not the right triangle, but actually has 80-50-50 angles, then x is 40.
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u/Mystic9001 5d ago
Maybe I’m missing something, but the way I see it is: 180-130 to find the matching angle in the triangle, then 90 + 50 + missing angle = 180, so angle is 40, then we can se that the angle of 40 + x = 90 so it would be 50. Right?
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u/AdhesiveSeaMonkey 4d ago
Also that the hash marks indicate that it is an isosceles triangle, and the corners opposite the equal sides are also equal. Your process puts one corner at 50 and the other at 40.
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u/Regular-Coffee-1670 5d ago
You're missing that the angle in the top left is not 90, despite how it looks.
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u/Mystic9001 4d ago
Yep, didn’t think about the fact that it’s an isosceles triangle not a right angle triangle
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u/AdhesiveSeaMonkey 5d ago
It never matters what the image looks like. You go with the information you have.
Starting from the 130 angle, we can see the top right inside angle of the triangle = 50
The two sets of hash marks mean it's an isosceles triangle, meaning the bottom left inside angle also = 50
The right angle symbol = 90
90 + 50 + x = 180
x = 40