The recommended pressure for a particular tire is 1.72 x 10^5 Pa (above atmospheric). You fill the tire when the temperature is 20 degrees C. How do I find the initial pressure and temperature on absolute scales in this case? Also what should the gauge pressure be after the tire has been driven for an hour on the freeway and has reached a temperature of 50 degrees C?

The absolute pressure is the same as presssure relative to atmospheric plus atmospheric - which is 1 Bar or 10^5 Pa - so add that to the relative pressure to get absolute pressure.

The absolute scale for temperature is Kelvins - add 273.15 to the temp in Celsius to get the temp in Kelvins.

The pressure and temperature in an enclosed tire should follow the Ideal Gas Law, so PV/T is a constant.