The correct answer is A. 45°.
A synchronous motor develops maximum power when the load angle is 45°. This is because the torque developed by a synchronous motor is proportional to the sine of the load angle. When the load angle is 45°, the sine of the load angle is 0.707, which is the maximum value of the sine function. Therefore, the synchronous motor develops maximum power when the load angle is 45°.
The other options are incorrect because they do not correspond to the maximum power point of a synchronous motor. When the load angle is 0°, the torque developed by the motor is zero. When the load angle is 90°, the torque developed by the motor is also zero. When the load angle is 120°, the torque developed by the motor is negative. Therefore, the synchronous motor does not develop maximum power when the load angle is 0°, 90°, or 120°.