To solve this, we can make a few equations:
For the first triangle on the left
4y -18 + y + 14 + 6x - 11 = 180
5y + 6x = 180 + 18 + 11 - 14
5y + 6x = 195
For the second triangle on the right
6x - 11 + x + 5 + 81 = 180
7x = 180 - 81 - 5 + 11
7x = 105
x = 15
5y + 90 = 105
5y = 15
y = 3
Therefore y is 3 and x is 15.
Hope that helps!!!!
Cheating in AoPS??
I won't solve it, but I'll give you a helpful start.
Clearly, if we add up everything, then we would overcount, which we do not want. We want to count things once and only once. (Sound Familiar)
Now, make an expression where you add up everyone. The subtract that by two times the people who did all languages. (I technically gave you the answer.)
Hope that helps!!!