What is the value of x?

Using a theorem (yes i forgot the name of the theorem), we know that because the angles opposite of the sides are congruent, the sides must be congruent aswell. Therefore:
3x - 24 = x + 10
Now solve, starting by using the addition and subtraction properties of equality:
3x - 24 + 24 = x + 10 + 24
3x = x + 34
3x - x = x - x + 34
2x = 34
Now, use the division property of equality:
(2x)/2 = (34)/2
x = 17
Therefore, x = 17.
Hope this helps! :)