Final answer:
To find the closest negative angle coterminal to 826°, keep subtracting 360° until you get a negative result. The closest negative coterminal angle to 826° is -254°.
Step-by-step explanation:
To find the closest negative angle coterminal to 826°, we need to subtract multiples of 360° (which is the complete rotation in degrees) from 826° until we get a negative angle. The process is as follows:
- Starting with 826°, subtract 360°: 826° - 360° = 466°.
- Subtract 360° again: 466° - 360° = 106°.
- Since we need a negative angle, subtract 360° one more time: 106° - 360° = -254°.
The closest negative angle coterminal to 826° is -254°.
To find the closest negative angle coterminal to 826°, we need to subtract 360° from 826° repeatedly until we obtain a negative angle. Subtracting 360° once gives us 826° - 360° = 466°. Subtracting 360° again gives us 466° - 360° = 106°.
Subtracting 360° one more time gives us 106° - 360° = -254°.
Therefore, the closest negative angle coterminal to 826° is -254°.