please help me and explain it to me😓

[dense harness]

you are given ABCD is a square
and from this information, along with given angles, you gotta determine angle a

can you think of one angle releated proerty of a square?

[pliant lava]

I also don't get it

help 😓

[austere hamlet]

sorry, i don't really understand😓

[pliant lava]

All corners are 90?

[dense harness]

yup

[pliant lava]

@dense harness

ok what next from there

[dense harness]

by that, I think you should be able to determine angle a

[pliant lava]

oh

[dense harness]

remember that sum of angles in a triangle is 180

[pliant lava]

oh i think i got it

[austere hamlet]

can you explain it to me, i am very newbie

[pliant lava]

I don't get it

[austere hamlet]

umm

[pliant lava]

let's think together 😭

[austere hamlet]

okayy😭

[pliant lava]

ok the corners are 90

[austere hamlet]

@dense harness Do you know?

[pliant lava]

so baf is 40

dae is 5???

[dense harness]

you do know that squares have parallel lines and 90 degree angles at coreners?
if you know that, you should be able to deduce the angle

[austere hamlet]

yeah

[pliant lava]

oh they have parallel lines? 😭

I forgo that 💀

[pliant lava]

does that mean we can find afe with this role

rule*

[austere hamlet]

how😭

[pliant lava]

well aed is 85

[austere hamlet]

I think so

[supple loom]

Focus on line segment BC. You can see that there are two lines extending from it (AF and FE) which means two linear pairs. Since we know that angle AFB is 50 degrees, and the sum of the angles of a triangle is 180 degrees, and we know that angle ECF is 90 degrees since a square is a rectangle, then we know that triangle EFC is a 30-60-90 triangle. So angle EFC is 60 degrees, so now subtract 110 (60+50) from 180 degrees to get 70 degrees,the missing angle, angle AFE. Now since there are 180 degrees in a triangle just subtract 45 and 70 from 180 and you get 65 degrees. Number D

👍🏿

[pliant lava]

how do you know that ecf is of that comp?

[supple loom]

?

[pliant lava]

I don't get how you know that it's 30 60 90

[austere hamlet]

right triangle

[pliant lava]

what are you cooking

[austere hamlet]

total 180

[pliant lava]

it could be ANY right triangle dude

how is it specifically the 30/60/90

[austere hamlet]

angle c is 90, e is 30

[pliant lava]

???????

@supple loom come back!!

[austere hamlet]

umm😭😭

[supple loom]

I'm back sorry

Getting ready for church

I have to go in 5 minutes

[pliant lava]

please teach my butt

it'll work

[supple loom]

Okay okay I gotchu bro

so there are three ways we can find this out. 1st is deductive reasoning, 2nd is assuming/inverse proof, and 3rd is doing other calculations for the entire square JUST to prove that the triangle is a 30-60-90. But also the problem doesnt state that its 'not to scale' so then we can assume that what looks like 30-60-90 is 30-60-90

[pliant lava]

true

[supple loom]

Of course there are more complex ways to find this but why use those when we can use these

[pliant lava]

also true

so this answer you got was assumption ? 🤔 😔

well

[supple loom]

Deductive reasoning

[pliant lava]

Fair enough bro

[supple loom]

deductive reasoning is affective assuming lol

🤣

[pliant lava]

fancy term for guessing 😓

i did use the rule right

[supple loom]

well assuming is based off of bias and opinion.

[pliant lava]

50deg had to be part of afe cuz if you 'drag' line cd down

[supple loom]

guessing is when ur just clueless

[pliant lava]

and then you subtract the 45 and 50 from 180 you end up with something close to 85

but it couldn't be 85 cuz there still was part of the angle afe left

so the closest most reasonable answer would be d

[supple loom]

you know if you read the proof i just gave you its simpler 😭

[pliant lava]

but it felt disgusting to guess

[supple loom]

isnt that what you just did...

[supple loom]

with these messages

[pliant lava]

is that what u did?

mb thn

[supple loom]

Well I used theorems and the definition of a square as proof

[lone estuary]

This problem is so not drawn to scale

[pliant lava]

I KNOW RIGHT

at least they could've made the square better

[supple loom]

okay FR tho

[lone estuary]

One of the angles i got was literally zero degrees

[pliant lava]

https://giphy.com/gifs/cooking-thanos-what-was-he-4F3KPZtQvVRBuAEk2Y

[austere hamlet]

@supple loom thank you very much for the explanation😁

[pliant lava]

at least he's happy I guess

[lone estuary]

It’s like a trap if you do not use theorems and stuff

[pliant lava]

flip a coin

[supple loom]

Ofc bro. I'm a freshman in high-school doing geometry so I'm just glad I could help someone. Shows me that I am actually understanding 😭

[dark lake]

i think all the possible combinations of alpha+z=135 can be teh answer

[lone estuary]

Have you guys reached any conclusion yet

[austere hamlet]

I'm in high school too, but I don't really understand this😔😮‍💨

[pliant lava]

I'm in my final year 😀

[lone estuary]

I am not going to read 80 messages so ima just ask yall

[pliant lava]

am I cooked?..

[olive iron]

in the end not enough info and all are guessing is what i think 🥀

[supple loom]

Ayyy

[pliant lava]

well wouldn't need geo in last year anyways

[lone estuary]

i got alpha equals 95 degrees

[austere hamlet]

we have found the answer

[pliant lava]

who's we

[lone estuary]

Ok nice

[lone estuary]

What did you get

[supple loom]

@lone estuary is ur pfp a bunny with a pancake on its head?! 🤣

[austere hamlet]

65°

[lone estuary]

Yes

Amazing isnt it?

[austere hamlet]

umm, how to make unsolved to solved

[austere hamlet]

do u know?

[lone estuary]

Not sure

[supple loom]

its beautiful

idk either lol

im new here

[dark lake]

how did you get that send soln

[austere hamlet]

.close

[trim olive]

Solved

Post marked as solved by @austere hamlet.

Use .unsolved if this was a mistake.

[austere hamlet]

Focus on line segment BC. You can see that there are two lines extending from it (AF and FE) which means two linear pairs. Since we know that angle AFB is 50 degrees, and the sum of the angles of a triangle is 180 degrees, and we know that angle ECF is 90 degrees since a square is a rectangle, then we know that triangle EFC is a 30-60-90 triangle. So angle EFC is 60 degrees, so now subtract 110 (60+50) from 180 degrees to get 70 degrees,the missing angle, angle AFE. Now since there are 180 degrees in a triangle just subtract 45 and 70 from 180 and you get 65 degrees. Number D

[olive iron]

if you are done with the thread and do not have any other query, you can close it by typing .close.
Closing solved threads/help channels helps people know that the query is solved and avoid the need to ask if you still need help

[supple loom]

Glad I could help @austere hamlet

[lone estuary]

How did you find that it was a 30-60-90 triangle

[dark lake]

yeah im also confused

[austere hamlet]

This

right angle c has 90°

[dark lake]

did you measure it?

[olive iron]

same

[austere hamlet]

from the picture it may not look like that, but it is already a right triangle.

[dark lake]

if the question was not to scale it was unsolvable.

[austere hamlet]

so there are three ways we can find this out. 1st is deductive reasoning, 2nd is assuming/inverse proof, and 3rd is doing other calculations for the entire square JUST to prove that the triangle is a 30-60-90. But also the problem doesnt state that its 'not to scale' so then we can assume that what looks like 30-60-90 is 30-60-90

[olive iron]

yes, but how do you know it is 30-90-60

[supple loom]

☝🏿

[lone estuary]

I don’t think assuming it was 30-60-90 was the way 😭

[austere hamlet]

umm, is there any good way other than that🤔

[olive iron]

even if figure is to scale the question wouldnt be solved by measuring/ assuming unless you were supposed measure the angles

[dark lake]

you are getting a linear equation in 2 variables and anything that follows on that can be a solution-> alpha+z=135

[supple loom]

You just use the theorems for right triangles to solve for all of their angles and then deduct for the inner triangle for angle alpha

their being the "outer" triangles

there was no guessing involved

i said that you CAN guess

but thats not what we did

[olive iron]

which theorem sorry couldnt backread all the messages

[supple loom]

The sum of the angles of a triangle is 180 degrees, the acute angles of a right triangle are complementary

Anyways guys I gtg to church now

@austere hamlet I'm glad I could help

Y'all have a great day!

[olive iron]

i dont understand how this gets to 30 -60-90

[dark lake]

he said it was not written that it was "not to scale" so he assumed it to be

@austere hamlet if you've got the actual solution I will appreciate if you send it

[austere hamlet]

actually i follow @zeta's opinion

I think that makes sense

[dark lake]

i am asking if you have your hands on the real solution?

[austere hamlet]

nope

[lone estuary]

So far I have not found a way

Where did you get this problem from

[flint hamlet]

maths doesn't work like that. you cant just assume its 30-60-90

no one has found a solution here cuz yall are guessing

[coral osprey]

Bro. Is the problem even correct by itself? Look at the triangle ABF. Since angle F there is equal to 50, then angle A is 40(since ABF is a right triangle). But, if you add up angles FAB and FAE, it is equal to 95. And then you would have to add it up to the angle DAE and you are getting an angle that is far more than 90 degrees, which is impossible for a square. The conditions by themselves are wrong.

[coral osprey]

Or, for the full angle A to be 90 degrees, angle DAE would have to be -5. Which is basically nonsense, cuz it's just physically impossible.

I dunno how you all solved this problem, but all the solutions are wrong, cuz the problem is incorrect by itself.

[coral osprey]

Wait.

Forget what I just told ya. It was nonsense.

[dense harness]

I think this might require an auxiliary construction

[covert parrot]

rotate the triangle ABF around A such that B->D and F->F'. Then the angle F'AE=90-45=45. So, the triangle F'AE is congruent to FAE, thus, alpha = angle AEF'=180-45-50=85.

[coral osprey]

Ah, now I have it. Okay, so let's begin with the triangle ADE. Angle A is 5° there, and angle E is 85°. Now, let's call angle E in the triangle EFC Gamma. Then, 85+Alfa+Gamma=180°. Or, Alfa+Gamma=95°. Now, angle F in the triangle EFC is 90-Gamma. Let's call the angle F in the triangle AFE Beta. Then, 90-Gamma+Beta+50°=180. Or, Beta= 40 + Gamma. Now, let's take a look at the triangle AFE. From there, we can tell that Alfa+Beta= 135. Now, a very universal method can work here. Just putting every choice instead of Alfa to see if everything is right there. Let's say Alfa is the answer A, which is 35°. Then, Gamma is 60, 90-Gamma is 30. Beta is equal to 100. All things right. Let's call the angle Alfa 40°. Then, Gamma is equal to 55°. 90-Gamma is equal to 35°. Beta is equal to 95°. All things are right, once again. Take Alfa as 55°. That means that now Gamma is 40°. 90-Gamma is 50. Then, Beta is 80°. Once again, nothing's wrong here. Take Alfa as 65°. Given that, Gamma is 30°, 90-Gamma is 60°. Beta is 70°, which is fine again. Finally, if Alfa is 85°, then Gamma is 10°, 90-Gamma is 80°. Beta is 40. All things fine once more. Hm... Honestly, all options seem kinda fine.

[coral osprey]

This seems a little tougher than it looks.

[supple loom]

Did you see my previous message about how you need to find the angles of the right triangles surrounding the main one?

if you find all of the angles of the surrounding polygons then you find the final angle

or you can just find the angles of the bottom right and top right triangles

there are many ways to solve it

[austere hamlet]

does that mean the question doesn't provide any additional information?

[flint hamlet]

FAB + FAE is 85

[coral osprey]

No. I don't think so. @covert parrot had the right method, but didn't elaborate on that too much. So, if possible, could you elaborate on that method?

[hot escarp]

think what he means is SAS congruency because F'A = FA and AE = AE and 45 = 45 because the triangle rotation combines angles BAF and DAE which add with FAE to become 90 degrees and since FAE is 45 degrees F'AE (which is BAF + DAE) is also 45 degrees.

this is what i thought was solution (55)

but it just doesn't make sense lol

for QD2718 solution

they share side AE and F'A is the same as FA because F' is the point after rotation around point A which does not modify the properties of triangle

so in that case a = 85

this question sucks bro

[dark lake]

https://youtube.com/shorts/CvL2z1hk6OA?si=iuSvDO4cy8bEEzFC I've seen these types of questions

[dark lake]

85 is the right answer indeed

[austere hamlet]

very make sense, it becomes easier for me to understand it

[austere hamlet]

but if the bottom right part of the right triangle is just thrown away, is there no problem?