To determine the final position of the arrow after a 185-degree counterclockwise rotation, we can visualize its movement on the circular arrangement of points L, M, N, O, P, Q, R, S.
Starting from the initial position of the arrow, we need to calculate how many positions it will move when rotated 185 degrees.
Each full rotation (360 degrees) corresponds to the total number of positions. Since there are eight points (L, M, N, O, P, Q, R, S), each position corresponds to an angle of:
\[ \frac{360 \text{ degrees}}{8 \text{ positions}} = 45 \text{ degrees per position} \]
Next, we need to find out how many positions correspond to 185 degrees.
To find this, we divide 185 degrees by 45 degrees per position:
\[ \frac{185}{45} \approx 4.11 \]
This means that the arrow will move approximately 4 full positions (the whole number part of 4.11) plus a little more.
Counting the positions from the starting point:
- 0 degrees: starting position (for example, say it's at L)
- 45 degrees: M
- 90 degrees: N
- 135 degrees: O
- 180 degrees: P
After moving 180 degrees to P, we still need to add the additional rotation of \( 185 - 180 = 5 \) degrees. 5 degrees is about one-eighth of a full position (since each position is 45 degrees). This means the arrow will move slightly into the next position.
Since P is the last whole position of our 180-degree rotation, and 5 degrees from it will lead it just past P towards Q.
Thus, after rotating 185 degrees counterclockwise, the arrow points between Q and P.
So, the correct answer is:
between Q and P