Angle related to different-sized, adjacent squares

[U123ui]

I should find alpha angle

 

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[Dr.Peterson]

I should find alpha angle

Yes, you should.

It sounds like fun; we'll be glad to help once we see where you need help.

 

[R.M.]

Is there a nice triangle you can create with the given information? HINT: yes there is. And if you can assume that the grid makes the figure a scale drawing, then the problem is even easier.

 

[R.M.]

Is there a nice triangle you can create with the given information? HINT: yes there is. And if you can assume that the grid makes the figure a scale drawing, then the problem is even easier.

Scratch the part about the scale; doesn't appear to make much sense.

 

[U123ui]

I have tried many times to find the angle and it works only through the cosine theorem and I would like a solution method that would be less time-consuming. Btw if need to send a solution I can

 

[R.M.]

I tried right & similar triangles, but despite telling my students to never do this, I assumed the scale was accurate. That led to some nasty contradictions. I'll go stand in the corner now. Good thing they don't read this site.

 

[U123ui]

I tried right & similar triangles, but despite telling my students to never do this, I assumed the scale was accurate. That led to some nasty contradictions. I'll go stand in the corner now. Good thing they don't read this site.

try using the sides and the cosine theorem, because the solution comes to me only this way

 

[Otis]

tried many times to find the angle and it works only through the cosine theorem and I would like a solution method that would be less time-consuming … if need to send [my] solution I can

Yes, please post your solution. You ought to always do that, when seeking feedback or comments on a solution that you've already found.
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[U123ui]

Yes, please post your solution. You ought to always do that, when seeking feedback or comments on a solution that you've already found.
$\;$

initially I wanted to see solution that could be much easier than mine

 

[Otis]

initially I wanted to see solution that could be much easier than mine

Okay, but how would people determine that, without first seeing your solution?
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[U123ui]

Okay, but how would people determine that, without first seeing your solution?
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I'm sorry, I didn't think about that
There is mine solution that seems creepy

 

[Dr.Peterson]

I'm sorry, I didn't think about that
There is mine solution that seems creepy

I don't see an answer there. What angle do you get?

I would have solved for the ratio b/a (or a/b), and used that to find the angle.

 

[lev888]

I'm sorry, I didn't think about that
There is mine solution that seems creepy

Start with your first equation but don't solve it for a or b, solve it for a/b.