要在Android设备上获取指南针方向的角度，可以使用SensorManager类和SensorEventListener接口。以下是获取指南针角度的步骤:
1.在Activity中实例化SensorManager：

private SensorManager sensorManager;
sensorManager = (SensorManager) getSystemService(Context.SENSOR_SERVICE);

2.注册SensorEventListener以监听方向传感器事件：

private SensorEventListener sensorEventListener = new SensorEventListener() {
    float[] gravity = new float[3];
    float[] geomagnetic = new float[3];

    @Override
    public void onSensorChanged(SensorEvent event) {
        if (event.sensor.getType() == Sensor.TYPE_ACCELEROMETER) {
            System.arraycopy(event.values, 0, gravity, 0, 3);
        } else if (event.sensor.getType() == Sensor.TYPE_MAGNETIC_FIELD) {
            System.arraycopy(event.values, 0, geomagnetic, 0, 3);
        }

        float[] rotationMatrix = new float[9];
        boolean success = SensorManager.getRotationMatrix(rotationMatrix, null, gravity, geomagnetic);

        if (success) {
            float[] orientation = new float[3];
            SensorManager.getOrientation(rotationMatrix, orientation);
            float azimuth = orientation[0];
            float degrees = (float) Math.toDegrees(azimuth);
            degrees = (degrees + 360) % 360; // 保证角度范围在0-360度之间
            // 显示指南针角度
            TextView compassTextView = findViewById(R.id.compass_text_view);
            compassTextView.setText("指南针角度：" + degrees);
        }
    }

    @Override
    public void onAccuracyChanged(Sensor sensor, int accuracy) {
        // do nothing
    }
};

sensorManager.registerListener(sensorEventListener,
        sensorManager.getDefaultSensor(Sensor.TYPE_ACCELEROMETER),
        SensorManager.SENSOR_DELAY_NORMAL);
sensorManager.registerListener(sensorEventListener,
        sensorManager.getDefaultSensor(Sensor.TYPE_MAGNETIC_FIELD),
        SensorManager.SENSOR_DELAY_NORMAL);

3.在应用程序关闭时注销SensorEventListener：

@Override
protected void onPause() {
    super.onPause();
    sensorManager.unregisterListener(sensorEventListener);
}

完整的代码示例如下：

public class MainActivity extends AppCompatActivity {

    private SensorManager sensorManager;

    private SensorEventListener sensorEventListener = new SensorEventListener() {
        float[] gravity = new float[3];
        float[] geomagnetic = new float[3];

        @Override
        public void onSensorChanged(SensorEvent event) {
            if (event.sensor.getType() == Sensor.TYPE_ACCELEROMETER) {
                System.arraycopy(event.values, 0, gravity, 0, 3);
            } else if (event.sensor.getType() == Sensor.TYPE_MAGNETIC_FIELD) {
                System.arraycopy(event.values, 0, geomagnetic, 0, 3);
            }

            float[] rotationMatrix = new float[9];
            boolean success = SensorManager.getRotationMatrix(rotationMatrix, null, gravity, geomagnetic);

            if (success) {
                float[] orientation = new float[3];
                SensorManager.getOrientation(rotationMatrix, orientation);
                float azimuth = orientation[0];
                float degrees = (float) Math.toDegrees(azimuth);
                degrees = (degrees + 360) % 360; // 保证角度范围在0-360度之间
                // 显示指南针角度
                TextView compassTextView = findViewById(R.id.compass_text_view);
                compassTextView.setText("指南针角度：" + degrees);
            }
        }

        @Override
        public void onAccuracyChanged(Sensor sensor, int accuracy) {
            // do nothing
        }
    };

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        // 实例化SensorManager
        sensorManager = (SensorManager) getSystemService(Context.SENSOR_SERVICE);

        // 注册SensorEventListener
        sensorManager.registerListener(sensorEventListener,
                sensorManager.getDefaultSensor(Sensor.TYPE_ACCELEROMETER),
                SensorManager.SENSOR_DELAY_NORMAL);
        sensorManager.registerListener(sensorEventListener,
                sensorManager.getDefaultSensor(Sensor.TYPE_MAGNETIC_FIELD),
                SensorManager.SENSOR_DELAY_NORMAL);
    }

    @Override
    protected void onPause() {
        super.onPause();
        // 在暂停Activity时注销SensorEventListener
        sensorManager.unregisterListener(sensorEventListener);
    }
}