Does the sun's rising/setting angle change every few months?
The Sun rises and sets at a different point on the horizon every day. The change is small, so without careful observations, it may take several days or weeks to be fully aware of the change. Mathematically, the position of rising/setting can be found from the following formula:
$$\cos(\theta) = -\frac{\sin(declination)}{\cos(latitude)}$$
where

$\theta$ is the angle measured from due south to the point on the horizon where the object rises. (The angle is the same for rising and setting, if you ignore the change in the Sun's declination during the day.)
declination ranges between approximately +23.5 and -23.5 degrees for the Sun during 6 months (southern hemisphere winter to summer) and then from -23.5 to +23.5 during the next 6 months.
latitude is the observer's latitude.

From 35° S latitude, the winter Sun would rise at $\theta=119$ from due south (or 61° from due north, approximately ENE). The summer Sun would rise at $\theta=61$ from due south (or 119° from due north, approximately ESE). The range is 119-61=58° along the horizon.
At latitudes closer to the equator (0° latitude), the difference is smaller. The range is approximately 47° along the horizon when at the equator. At latitudes closer to the poles, the range becomes larger. At the Arctic and Antarctic Circles, the range is the largest that it can be: 180° (at least mathematically). At these high latitudes, the diameter of the Sun and refraction become important to calculate the precise location of rising.