Lines of longitude are closer together near the poles and further apart at the equator, because they are defined as lines which pass through the poles.

But lines of latitude are defined as being parallel to the equator. This means that a degree of latitude is the same distance anywhere on Earth.

As to the actual distance, you need to look up the polar circumference of the Earth and divide by the number of degrees (or minutes or seconds) of longitude through which you would pass on a journey around the Earth starting at one of the poles.