Neela’s clock is broken. The minute hand rotates around the clock correctly, but the hour hand is stuck in the three o’clock position. Suppose Neela first looks at the clock when the hands are aligned and it shows 3:15. She looks at the clock again and sees that the hour and minute hands of the clock form the arms of an angle measuring −105°. Through which of the following could the minute hand have rotated to reach its current position?
−465°
−375°
−435°
−95°
@tkhunny

Question

Neela’s clock is broken. The minute hand rotates around the clock correctly, but the hour hand is stuck in the three o’clock position. Suppose Neela first looks at the clock when the hands are aligned and it shows 3:15. She looks at the clock again and sees that the hour and minute hands of the clock form the arms of an angle measuring −105°. Through which of the following could the minute hand have rotated to reach its current position?
−465°
−375°
−435°
−95° 
@tkhunny

tkhunny · Answer

-105º
-105º - 360º
-105º - 2*360º
Etc.

anonymous · Answer

Thank you, It didn't make much sense to me. I kept trying to figure out what the measurement was when the clock was at 3:15 first.

anonymous · Answer

I'm still confused could someone help me?

anonymous · Answer

If the clock is showing 3:15, the hands are on top of each other which means that there is no angle, correct? |dw:1354811778137:dw|

anonymous · Answer

@UnkleRhaukus

tkhunny · Answer

Or the angle is 0º or 360º or 720º or -360º or etc.  Any difference of this sort suggests they are at the same location.

anonymous · Answer

The answer was -465 degrees.

tkhunny · Answer

So, -105º - 360º = -465º?  That looks very familiar.

anonymous · Answer

Yes, thank you guys for you help!