An angle in the standard (x,y) coordinate plane has its vertex at the origin and its initial side on the positive x-axis If the measure of an angle in standard position is `(1,314^@)`, it has the same terminal side as an angle of each of the following measures EXCEPT:

Options

A. `594^@`
B. `314^@`
C. `234^@`
D. `-126^@`

Answer

To solve the problem, we need to find which angle does not share the same terminal side as the angle of \( 1314^\circ \). We can do this by reducing \( 1314^\circ \) to an equivalent angle within the range of \( 0^\circ \) to \( 360^\circ \).

### Step-by-Step Solution:

1. **Find the equivalent angle of \( 1314^\circ \) within \( 0^\circ \) to \( 360^\circ \)**:
- Since angles are periodic with a period of \( 360^\circ \), we can subtract \( 360^\circ \) repeatedly from \( 1314^\circ \) until we get an angle within the desired range.
- First, subtract \( 360^\circ \):
\[ 1314^\circ - 360^\circ = 954^\circ \]
- Subtract \( 360^\circ \) again:
\[ 954^\circ - 360^\circ = 594^\circ \]
- Subtract \( 360^\circ \) again:
\[ 594^\circ - 360^\circ = 234^\circ \]
- Now, \( 234^\circ \) is within the range of \( 0^\circ \) to \( 360^\circ \).

2. **List the angles to check against the options**:
- The equivalent angle of \( 1314^\circ \) is \( 234^\circ \).
- Now we need to check the options given in the problem to see which angle does not share the same terminal side as \( 234^\circ \).

3. **Evaluate the options**:
- **Option 1**: \( 594^\circ \) (shares terminal side with \( 234^\circ \))
- **Option 2**: \( 954^\circ \) (shares terminal side with \( 234^\circ \))
- **Option 3**: \( 234^\circ \) (same angle)
- **Option 4**: \( -126^\circ \) (find the equivalent positive angle)
- To convert \( -126^\circ \) to a positive angle:
\[ -126^\circ + 360^\circ = 234^\circ \]
- This also shares the same terminal side.

4. **Identify the angle that does not share the terminal side**:
- The only angle left to check is \( 314^\circ \). We can check if it shares the same terminal side:
- Subtract \( 360^\circ \) from \( 314^\circ \):
\[ 314^\circ - 360^\circ = -46^\circ \]
- The equivalent positive angle for \( -46^\circ \) is:
\[ -46^\circ + 360^\circ = 314^\circ \]
- Since \( 314^\circ \) does not equal \( 234^\circ \), it does not share the same terminal side.

### Final Answer:
The angle that does not share the same terminal side as \( 1314^\circ \) is \( 314^\circ \).