Zoot Allures wrote:I don't know what you mean by identical ...

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.

Zoot Allures wrote:... but I'm not big on geometry ....

And geometry is not enough.

The main part of the task is not a geometrical one, by the way.

Zoot Allures wrote: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.

What I mean is easily to find out by the text and the picture of my post:

I wrote:Your watch has stopped. So it does not work anymore. The little hand of the watch indicates approximately ten o'clock, and the big hand of the watch indicates approximately two o'clock. Both hands of the watch form an identical angle. When did your watch stop precisely?

Zoot Allures wrote:Draw a line from the nut in the middle of the clock that bolts the hands down to the 12.

No.

Zoot Allures wrote:There is your axis line. So each hand would have the same angle relative to the line.

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:

Zoot Allures wrote: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.

Zoot Allures wrote:... but I'm not big on geometry ....

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:

Zoot Allures wrote: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.

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:

I wrote:Your watch has stopped. So it does not work anymore. The little hand of the watch indicates approximately ten o'clock, and the big hand of the watch indicates approximately two o'clock. Both hands of the watch form an identical angle. When did your watch stop precisely?

Zoot Allures wrote:There is no such thing as an identical angle because all angles can be identical depending on the axis line between them.

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.

Zoot Allures wrote: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.

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.

Zoot Allures wrote:Really, mentioning that the angles are identical seems to be superfluous here.

No. It is exactly the opposite that is true.