A spinner turns 7077 degrees. The spinner would have ended up at the same spot if it had turned only:
a) 77 degrees.
b) 2197 degrees.
c) 4377 degrees.
d) 4917 degrees.
e) 5537 degrees.
each rotation is 360°
7077/360 = 19.65833...
so we have 19 full rotations and .658333.... of a rotation
2197/360 = 6.102.... , not the same decimal
4377/360 = 15.158... , no
4917/360 = 13.658333.. , ahhh, the same decimal
5537/360 = 15.38... , no
So it looks like 4917° ends up in the same place
Which of these numbers differs from 7077 by a multiple of 360?
4917 = 7077 - 6*360
To determine the equivalent angle, we need to divide the given angle (7077 degrees) by 360 degrees (a full revolution).
Using the remainder after division, if the spinner ends up at the same spot, the remainder should be 0.
1) For option a) 77 degrees:
7077 degrees ÷ 360 degrees = 19 remainder 237
The remainder is not 0, so option a) is not correct.
2) For option b) 2197 degrees:
7077 degrees ÷ 360 degrees = 19 remainder 237
The remainder is not 0, so option b) is not correct.
3) For option c) 4377 degrees:
7077 degrees ÷ 360 degrees = 19 remainder 237
The remainder is not 0, so option c) is not correct.
4) For option d) 4917 degrees:
7077 degrees ÷ 360 degrees = 19 remainder 237
The remainder is not 0, so option d) is not correct.
5) For option e) 5537 degrees:
7077 degrees ÷ 360 degrees = 19 remainder 237
The remainder is not 0, so option e) is not correct.
Based on these calculations, none of the given options would result in the spinner ending up at the same spot.
To determine the answer to this question, we need to find the smallest positive number that is congruent to 7077 degrees modulo 360 degrees.
First, let's understand what it means for two angles to be congruent modulo 360 degrees. If two angles have the same measure modulo 360, it means that when you add or subtract multiples of 360 from the angles, they would end up at the same spot.
In this case, we want to find the smallest positive angle that, when added or subtracted a multiple of 360 degrees, would end up at 7077 degrees.
We can start by subtracting 7077 degrees by multiples of 360 degrees until we get a positive angle less than 360 degrees:
7077 - 1 * 360 = 6717 (not less than 360)
7077 - 2 * 360 = 6357 (not less than 360)
7077 - 3 * 360 = 5997 (not less than 360)
7077 - 4 * 360 = 5637 (not less than 360)
7077 - 5 * 360 = 5277 (not less than 360)
7077 - 6 * 360 = 4917 (less than 360)
We can see that when we subtract 6 * 360 from 7077, we get an angle less than 360 degrees.
Therefore, the answer is option (d) 4917 degrees.