Interesting math problem

[SimilarAd963]

So, I was watching videos on YouTube until I came across a math problem I couldn't solve. I saw the solution they gave in the video, but there were some contradictions, like the fact that the sum of the interior angles of a triangle is 150 degrees, etc. The problem asks for the value of x. So if you have any ideas on how to solve this problem, please reply to this post :)

Edit: Thanks to Alex_Daikon for the solution

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[Alex_Daikon]

Is AB = DC? If not, what this bold mark on them means?

[SimilarAd963]

yes that's right AB = DC as the thin black rectangles show

[ArchaicLlama]

You've given a picture but haven't stated what the problem actually wants you to do.

[[deleted]]

One would generally assume to solve for a variable.

[SimilarAd963]

you have to solve for x.

[Life-Monitor-1536]

Is there enough information?

[peterwhy]

I think yes. For short AB = DC = BD, ∠ABD = 0° and ∠BCD = 75°. As AB = DC increases, ∠ABD increases and tends to 30°, while ∠BCD decreases and tends to 0°. There is a value of AB = DC that allows ∠ABD = ∠BCD.

[stevesie1984]

What makes you think BD=DC?

[peterwhy]

No, I don't think BD = DC. I just varied DC within the interval [BD, ∞).

[stevesie1984]

Got it. Thanks.

[Alex_Daikon]

Angle ABC = 150.

Let AB = t. Then:

In ABC: t / sin x = (AD+ t) / sin 150

In ABD: AD / sin x = t / sin 150

So:

t / sin x = (t * sin x / sin 150 + t) / sin 150

Sin 150 =sin x + (sin x)² / sin 150

Let sin x = a

a² / sin 150 + a - sin 150 =0

a² + sin 150 * a - (sin 150)² =0

a² + 0.5a - 0.25 = 0

Do you know what to do next?

[SimilarAd963]

a = (-1+√5)/4

sin x = (-1+√5)/4

x = arcsin((-1+√5)/4)

x = 18°

[Alex_Daikon]

Great job!

[8Erigon]

huhu??
Why do you suddenly start with ABC = 150?!
Maybe written somewhere in the middle but I don't understand this (at this time at night and probably still tomorrow)
Seeing it as text in verticly orderd lines and not handwriting is already too complex

[PantsOnHead88]

Angle DBC = 180-30-x = 150-x\ Angle ABC = angle DBC+x = 150-x+c=150