Lines angles and proofs

[spiral tapir]

Hi need help on this one question I don't quite get

[spiral tapir]

<@&286206848099549185>

[boreal stratus]

Where is c?🤔

Also is this a test?

[spiral tapir]

Practice test teacher left

For tomorrow

[spiral tapir]

I have no idea

Oh wait

[boreal stratus]

Alr

[boreal stratus]

In these kind of questions
The first thing you would like to do is find triangles or any shapes where you know the total angle

In this case we have triangles

In which triangle do you think we can find the missing angle

[spiral tapir]

Erm idk

[spiral tapir]

I didn't got full instructions on this

Teacher jumped from this

[boreal stratus]

Let me rephrase it in which triangle do we have 2 known angles and an unknown angle ?

[spiral tapir]

HFD?

[boreal stratus]

Yep

So now you can get the value of HDF
Agreed?

[spiral tapir]

Yea

[boreal stratus]

So what's the value

[spiral tapir]

11

110

[boreal stratus]

Nice

Now since we know angle angle HDF and we also know that BDF is a straight line
Which angle can we get from it

[spiral tapir]

Is that 180-110-30?

[boreal stratus]

No no

First name what angle it is

[spiral tapir]

What 😭

[boreal stratus]

Did you read this?

[spiral tapir]

Hmm is it angle angle side

Or am I way too far off

[boreal stratus]

Like is it ABC or DHF or smth like that

[spiral tapir]

Ahh

BDF?

Or

BHF

[boreal stratus]

Let's start again

[spiral tapir]

Which is the bigger triangle

Ok

[boreal stratus]

If we know a line in this case BDF is a straight line

What is the value of angle BDF

[spiral tapir]

180

?

[boreal stratus]

Yes!

[spiral tapir]

Ah

[boreal stratus]

Now
BDF = BDH+HDF
Agreed ?

[spiral tapir]

Yea

[boreal stratus]

We know 2 of the values in this

Which are

[spiral tapir]

BDH and HDF?

[boreal stratus]

Yes

[spiral tapir]

Is each one 90?

[boreal stratus]

No

[spiral tapir]

😭

[boreal stratus]

You just said the value of BDF is 180

[spiral tapir]

Yes

[boreal stratus]

And you found out earlier that HDF is 110

[spiral tapir]

Ahhhhhhh

[boreal stratus]

So what's the value of angle BDH

[spiral tapir]

90

No

70

Mb

[boreal stratus]

Yes

Cool

[spiral tapir]

I'm kinda dumb 😭

[boreal stratus]

It's fine as long as you try

Are you familiar with the idea of opposite angles being equal?

[spiral tapir]

Nope

[spiral tapir]

Does that mean def = 70?

[boreal stratus]

You can't have an angle DEF

[boreal stratus]

It's fine we can do it the other way

We know that the angle BDH is 70

We just found that

[spiral tapir]

I thought u meant these are opposite angles being equal

[boreal stratus]

Let's consider the line HDE
We can say
HDE+BDH+BDE
Agreed?

[spiral tapir]

Yea

[boreal stratus]

You are right but the angle can be called either EDF or FDE but for DEF

[boreal stratus]

Let's skip it since you know opposite angles being equal

[boreal stratus]

This is what i meant

[boreal stratus]

So now we get angle FDE who's value is?

[spiral tapir]

70?

[boreal stratus]

Yep since both angles are equal

Now we check the same place
We have another pair of opposite angles which are?

[spiral tapir]

BDE and HDF

110

[boreal stratus]

Yes!

Alr until now we found out angles BDE , HDF,BDH , BDE

[spiral tapir]

Yes

[boreal stratus]

Let's now consider Angle BHF

What do you think it's value is

[spiral tapir]

Is it the sum from angle BDH and dhf

110+70?

[boreal stratus]

No

[spiral tapir]

Oh

[boreal stratus]

Do you know what that means?

[spiral tapir]

Is it just 90?

[boreal stratus]

Yes

[spiral tapir]

BHF=90?

[boreal stratus]

So you get the fact that BHF is also 90?

[boreal stratus]

Yes

What angle do you think we can find from here?

[spiral tapir]

HIJ?

[boreal stratus]

Try splitting BHF into sum of 2 angles

[spiral tapir]

Since it's opposite side

[boreal stratus]

It's angle IHJ

[spiral tapir]

90+110

[boreal stratus]

Yes but we can also find another angle

[boreal stratus]

No

[boreal stratus]

BHF = BHD+DHF

Get why?

[spiral tapir]

A little bit

[boreal stratus]

Uh

[spiral tapir]

I don't know what u mean by split in 2

If it's not like that or the sum of the 2 angles

[boreal stratus]

Just like we had it over ehre

[boreal stratus]

I meant the sum of what angles would give you angle BHF

[spiral tapir]

BDH and DHF

[boreal stratus]

Why BDH

[spiral tapir]

I thought these 2 made the whole triangle

[boreal stratus]

They do
But the angle red is BHD and not BDH

[spiral tapir]

Isn't that the same

[boreal stratus]

No

Order matters

[spiral tapir]

Ah

Didn't knew

[boreal stratus]

Get it?

[spiral tapir]

Ah

I meant then bhd

And HDF

The sum of it

Makes angle HBF

[boreal stratus]

You got this wrong again

[spiral tapir]

😔

[boreal stratus]

It's ANGLE BHF and not HBF

Now just substitute the know values

[spiral tapir]

Wdym

[boreal stratus]

Angle BHF = BHD+DHF
yk BHF is 90 and DHF is given as 40

[spiral tapir]

40+90 then?

[boreal stratus]

90=BHD +40
BHD = 90-40 =50

[spiral tapir]

ah

[boreal stratus]

I have to go
Got a class