in the diagram below given that XY = 30cm, XZY =30° and YZ = x, is it possible to solve for x using the theoram of pythagoras​

No, you need to know another  angle to prove that it is a right triangle to use the Pythagorean theorem.

If you did have an additional side length, that needed angle could be calculated and then use the Pythagorean to prove.

not enough information

step-by-step explanation:

we cannot know this, because the other students could have handed out 10 flyers, or they could have handed out 100. one way, the mean would go up, and another way, the mean would go down.