The distance between the two villages is 180 km, the cyclist traveled 9/10 of this path, how much distance is left for him to travel.

1) Let us find out what distance the cyclist covered, if it is known that 9/10 of the entire path, and the entire distance is 180 km.
180 * 9/10 = 162 km.
2) We find out the remainder of the not covered path, if we know that the entire distance is 180 km, and we learned that the cyclist has covered 162 km.
180 – 168 = 18 km.
Answer: the remainder of the route not covered was 18 km.