Find the smallest number of acute angles which add up to a full angle. Same with obtuse angles.
I've got this problem, and I tried to solve it, but I don't know if my reasoning is correct, and formal enough.
- Acute: In the case of acute angles, I intuit that the closer the angles are to $90°$, without being $90°$, the less will be needed to add up to $360°$, so if I add $x°|89≤x<90$, four times, this is $4x°|89≤x<90$, I will add up as minimum to $356°$, and what's left would be, it wouldn't matter if I chose $x=89°$ or $89°<x<90°$, another acute angle. So it seems like the less number of acute angles that add up to $360°$, is 5 angles.
- Obtuse: Here, I intuit that the less number of obtuse angles that add up $360°$ would be 2, this is because the bigger obtuse angle I can have, without the remaining angle becoming acute is $y|269°≤y<270°$, because if it was $270°$, or bigger, then the remaining angle would be either straight or acute, so $y+w= 360°$ and given the aforementioned conditions, it could be assured that both are obtuse.
Now, this is based more on intuition than anything else, I want to know if this is correct, and if it's formal enough.
Thanks in advance.