Since angles ∠X and ∠Y are corresponding angles created by the transversal cutting parallel lines, they are equal:
\[ ∠X = ∠Y \]
We can set up the equation:
\[ 5x + 30 = 3x + 60 \]
Now, we will solve for \( x \):
- Subtract \( 3x \) from both sides:
\[ 5x - 3x + 30 = 60 \] \[ 2x + 30 = 60 \]
- Subtract 30 from both sides:
\[ 2x = 60 - 30 \] \[ 2x = 30 \]
- Divide both sides by 2:
\[ x = \frac{30}{2} \] \[ x = 15 \]
Thus, the value of \( x \) is \( \boxed{15} \).