This has to be a trick question. Arminius is too smart to ask a question that is so obviously answered with “10:00 is when the clock stopped.” So, what’s the trick dude? Nobody’s playing so just give us the answer mmkay?
And what is an identical angle, anyway?
I think it is a little bit too early to give you the answer.
Both angles have the same degree. The angular degree is the same.
I don’t know what you mean by identical, but I’m not big on geometry, so I’ll explain my dumbed down misunderstanding of your statement.
If you mean each angle leaves its point of origin with the same degree relative to a line or axis drawn between them, then yeah, you have two congruent lines. But you can do this with any two angles leaving the same point of origin if you place a line directly between them.
Draw a line from the nut in the middle of the clock that bolts the hands down to the 12. There is your axis line. So each hand would have the same angle relative to the line. It would be a little more than a 45 degree angle for each hand, since the 3 and 9 would be a 90 degree angle while the 12 would be no angle.
No matter where you put the hands, you could draw a line directly between them, creating the same degree of each angle. That’s why I don’t understand what you mean when you say identical.
There is no such thing as an identical angle because all angles can be identical depending on the axis line between them.
Now if you insist that the 12 be the axis line, then putting the little hand on the 6 and the big hand on the 3, you would not have identical angles. The little hand would have a 180 degree angle while the big hand would have a 90 degree angle.
Really, mentioning that the angles are identical seems to be superfluous here.
If there are only two lines in a circle, the only two angles that can be the same is 180, that’s be either 0915 or 1445. You need another line.
Wait what? You lost me.
Draw a circle. Put a dot in the very center. Draw one line from that dot in any direction until it reaches the perimeter of the circle. Draw another one from that dot in any direction until it reaches the perimeter. Then put an axis directly in the middle between those two lines. Both of the two lines will proceed at exactly the same angle away from the axis between them.
I need a graphic. Somebody who knows what the hell I’m trying to explain here, please go find a graphic and post it.
The mathematical meaning of the adjective “identical” is identical with the mathematical meaning of the adjectives “same” and “equal”.
Please look at the watch again:
There is no doubt. The same angular degree. The two hands of the watch have the same angle. Which one it is is easily to find out.
And geometry is not enough. 
The main part of the task is not a geometrical one, by the way.
What I mean is easily to find out by the text and the picture of my post:
No.
The 12 is the axis line, but that is already clear because of the text and because of the picture. Here comes the picture again:
Geometrically “no angle” is not possible.
The equivalents betweenn the numbers of the watch and the degree values:
0 <=> 0°.
1 <=> 30°.
2 <=> 60°.
3 <=> 90°.
4 <=> 120°.
5 <=> 150°.
6 <=> 180°.
7 <=> 210°.
8 <=> 240°.
9 <=> 270°.
10 <=> 300°
11 <=> 330°.
12 <=> 360°.
Look at the watch again:
Yes, I know, but that is irrelevant. Again: What I mean is easily to find out by the text and the picture of my post:
You know from your own language that the 12 is always the pivotal point. For example: You know what it means when you say “12 o’clock”, “3 o’ clock”, or “5 past 12”, “5 past 3”, … and so on. “12 o’clock” <=> where are both hands of your watch? “5 past …” Why “5”? … You know? It is always with reference to the 12.
If the pivotal point was (it is not!) “half past 4”, then both would have identical angles (45 degrees, by the way - but according to the logic/mathematics and technique of all watches your example it is not possible, by the way). It is a tiny part of the task that one has to know what the pivotal point of a watch is.
No. It is exactly the opposite that is true.
No.
I understand everything you’ve said clearly. We are on the same page on that part. What I don’t understand is why any mention of the angle is relevant to the problem.
If the big hand is on 10 and the little hand is on 2, and the watch functions like every other watch in the known universe, and the watch has stopped working, then it stopped working at 10:10.
Now when you reveal the trick and I go ‘ohhhhhhh!’, I’m going to smack you. Now spit it out.
Graph the two angles.
If a rooster laid an egg on the top of a 10/12 pitch roof facing north, and an easterly wind of twenty mph was blowing, which side of the roof would the egg roll down?
Wow … leave it to Zoot to livin things up … 
Arminius obviously meant “the angles from 12 to the hour hand and 12 to the minute hand are identical when it stopped”.
The answer:
[tab]Dubiously assuming that I did the tiny bit of math right:
Time on Clock = 10:9:13.8461538461538[/tab]
But you have to figure out how to find it.
You have to read precisely. Your example here is not my example.You example does not work because of the logic/mathematics and technique of all watches, as I already said.
Again:
Oh, it’s one of those problems. An exercise in Zeno’s paradox. Infinite decimals and shit. Is it almost 10:10, almost almost 10:10, or almost almost almost 10:10? Holy moly, you can keep dividing the spaces between the minutes like… infinitely!
And I thought this was going to be something good.
Zeno or no, it is simple algebra/geometry.
That is obviously your job. You need to do it. Perhaps you will have the effect of learning by doing.
Nevertheless:
Nuh-uh, because at a smaller level, the noise that composes the sub-atomic particles that compose the atoms that compose the molecules that compose the elements that compose the material that the hands are made of are still moving.
I told you it was a trick.
Your premise did not specify an angle between a clock arm and 12. That’s what I mean by “you need another line”.
You have not understood it.
Show me the way of the solution, loudmouth. You have not understood it. This shows me your reaction. Again: Show me the solution process of the task. As I said: it is geometry, algebra, thus mathematics, and it is reading precisely, understanding the text, the logic and common sense in it, thus it is also linguistics. But the core of the task is mathematics. And you have not understood it.
This thread is about mathematics! What do you expect? Wonders? Miracles? “Something good”?
It was no trick.
No. If you meant it, then you would have said it. In addition: another line is not needed.
One has to figure out that the 12 is this “line” you are talking about. That is common sense but has nothing to do with the mathematical task. The text of my post was clear. It is your problem, if you are not capable of imagine a line.