The molecules of a gas at constant volume are somehow given a lower average kinetic energy.
what two measurable properties of the gas will change and in what direction?

Kinetic energy is proportional to temperature. An increase in the average kinetic energy, decrease the temperature and vice versa. pressure and temperature have a direct relationship between them, if temperature decreases, pressure also decreases and vice versa.

Explanation:

This concept is explained by taking into consideration the gas laws; GayLussac's law of combining volume and charles's law . considering the molecules of a gas at constant volume, there is a direct relationship between the pressure and temperature at constant volume, this is what gay lussac's law entails i.e gases who combine at constant volume they do so in fixed ratio and to the volume of their container.

As for charles's law, there exist a Volume - Temperature relationship at constant pressure, because volume and temperature have a direct relationship, when the average kinetic energy of gas molecules is decreased, this in turn decreases the temperature of the gas molecules.

And when the temperature decreases as a result of decrease in the average kinetic energy, this automatically affect the pressure thereby causing a reduction in the pressure of the gas container.

However, if the average kinetic energy of the gas molecules is increased again, then there will be an increase in the temperature and pressure and vice versa. Kinetic energy and temperature also have a direct relationship.