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[lost silo]

They are asking to find sum of angles but I do not understand how to???

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[lost silo]

I can't figure it out

[lost silo]

Hello

hi

So we are asked to find the sum

yes

alpha + betta + gamma

Let me just draw it on my book real quick

ok ty

[flat hull]

β = 2 * arcsen(1/sqrt((3^2)+1)) = 36,86 degrees

[lost silo]

no without arcsin

No trigonometry

[lost silo]

I gotchy

Answersheet says 90 degrees

but idk why

Alpha and gamma are the same

In magnitude

How do we know that though

just from observation?

That's because their sides are the same length

oh yeah mb

yeah yeah

Yeah observation

what about betta

They're just mirror images

It's easy, I think but tricky to see

I couldn't figure it out

Alpha + beta is 90

How

[grand glen]

||Circumcircle||?

[lost silo]

Beta can be figured out by tan function

Assuming each box to be a 1*1

Tan(beta/2) = 1/3

wait

you notice that these

are 90

degrees

look wait

Yes

That's the reason we gotta do trigo

Tan (alpha) =1/2

Tan (gamma)=1/2

if alpha + betta is = 90

then the answersheet must be wrong even though it is not

and this must be done without Trigonometry

[flat hull]

Alpha + Betts ain’t 90…

[lost silo]

thats what im saying

[flat hull]

It’s 2* Alpha + Betts = 90

[lost silo]

ye

[grand glen]

Or ||trapezoid||

[lost silo]

but why though

[lost silo]

alpha + betta + gamma

we have to find tht

[lost silo]

Let me cook

[grand glen]

Because ||parallelogram|| and some geometry

[lost silo]

where do u see parallelogram here?

[flat hull]

Because, the angle that Betta/2 + alpha = 45 degrees since it cuts in half the square

[grand glen]

I swear, just draw any singular relevant shape

[lost silo]

oh u mean that

It's 90

[grand glen]

The right line that contains beta, and the left line that contains alpha

[lost silo]

Created and shared using Adobe Scan.

let me see

[lost silo]

Here

So are we not able to do it without Trigo?

[lost silo]

That would just make us assume stuff

We can though

[grand glen]

This is a very nice problem

Can I please note a few things?

[lost silo]

Is my solution valid?

[lost silo]

@grand glen

[flat hull]

It is

[lost silo]

answer is right

[lost silo]

Alr

pi/2 is 90 degrees but im trying to figure out to do it without trigo lol

[grand glen]

1. Prove that alpha=gamma using inscribed triangles
2. Use parallelograms/valid shapes to find a relation between beta and alpha/gamma
3. Kill the problem by making a system of equations

Note that in parallelograms, opposite angles are congruent and adjacent angles add to 180 degrees

[lost silo]

Where is the parallelogram?

yes I do know that

why are these equal?

[lost silo]

Nope

Here

[lost silo]

That's some invalid stuff I wrote

No the betas ain't equal

My bad

[flat hull]

Wait, those in the middle ain’t right angles

[lost silo]

alr

[lost silo]

They are

[lost silo]

they are

It's a square grid

square grid

diagonal

s

[grand glen]

If only I could draw it out...

[lost silo]

create right angle

This is such a tedious problem

[grand glen]

Transversal laws.

[flat hull]

mb, yeah, confused

[grand glen]

Do you know what transversals are?

[lost silo]

,w transversals

[eager hemlock]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by draydengaurdiola

[lost silo]

Ohh nvm

Like a traversal line

I might not know English

[grand glen]

I’ll be home in a few minutes and I’ll draw out my hints/solutions

[lost silo]

What does transversal law

state?

[grand glen]

Draw 2 parallel lines.

[lost silo]

oh yeah

I do know those

yes

[grand glen]

Ok.

Understand now?

[lost silo]

The angles are equal

But that would make it beta/2

Im not sure how to connect those cause the angles are not on direct straight line

No it is ß

Yeah it is ß

My bad yeah

[lost silo]

Wdym?

I meant abt

parallel

lines

If the lengths are equal, the angles are equal too

[lost silo]

Use this property

[lost silo]

I know that

let me look at betta again

Nope

[lost silo]

Still can't figure out the relation

between betta and those 2 alphas

[flat hull]

Since red is alpha blue is Betts and yellow is 90 degrees

All adds up to 180

done

[lost silo]

wait

[grand glen]

Alright

[lost silo]

why is red alpha?

[grand glen]

I'm home

[grand glen]

Because of transversal laws

[lost silo]

Oh

the paralleogram

ah

[flat hull]

Thx

[lost silo]

now I see it

[grand glen]

Yes

[grand glen]

The proof is quite ambiguous here

[lost silo]

tysm

y'all

I am such an idiot

how could I not see that

😭

[grand glen]

Let me send what I have

[flat hull]

Yes, I was drawing on my phone

[grand glen]

There are pretty obvious congruency laws from this

1. alpha=gamma

[lost silo]

it makes sense now

thanks

I also have one more

which I couldn't figure out

[grand glen]

Ok

[lost silo]

The length of a side of an equilateral triangle ABC is 120. The segments BD, DE
and EF divide the triangle into 4 triangles with areas
equal to each other. What is the length of the segment F C?

What I tried to do here is find the ABC triangle area then divide into 4

but after that

I wasn't sure how I had to continue

[grand glen]

Hmm. Do you know the 1/2*b*h formula?

[lost silo]

yes

[lost silo]

btw the answer says 45

[tender pond]

@lost silo

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Hello alex_the_nerd, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.

[tender pond]

@grand glen @lost silo The user still needs help with this help request.

[lost silo]

Specifically this