What is the standard angle if 15 degrees, South of East

The phrase "15 degrees South of East" indicates a direction starting from the East and then moving 15 degrees toward the South. To express this direction as a standard angle (measured counterclockwise from the positive x-axis, which points East), we perform the following steps:

1. **Standard Position of East**: East corresponds to a 0-degree angle.
2. **Adjust for 15 Degrees Southward**: Moving South from East means subtracting 15 degrees from the East direction.

Therefore, the standard angle is:
\[
0^\circ - 15^\circ = -15^\circ
\]

Since standard angles are typically expressed as positive measurements between \(0^\circ\) and \(360^\circ\), we can convert \(-15^\circ\) into a positive angle by adding \(360^\circ\):

\[
-15^\circ + 360^\circ = 345^\circ
\]

### Conclusion
The standard angle for "15 degrees South of East" is **345 degrees**.

Would you like more details on this, or do you have any other questions? Here are some related questions you might find interesting:

1. What is the standard angle for 30 degrees North of West?
2. How do you convert directions like "Southwest" into standard angles?
3. What is the difference between standard position and bearing angle?
4. How do you calculate the standard angle for a given compass direction?
5. How can you determine the quadrant of a standard angle?

**Tip**: When converting directional angles into standard form, always start from the positive x-axis (East) and move counterclockwise for positive angles.

What is the standard angle if 15 degrees, South of East?

Learn how to determine the standard angle for a direction of 15 degrees South of East. This problem involves key trigonometric concepts and the calculation of angles in standard position, making it ideal for students in Grades 9-12.

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