To solve this problem, we need to make the two given angles (x + 12) and x + 48 supplementary because supplementary angles (adding up to $180^\circ$) ensure that the two lines $A$ and $B$ are parallel when intersected by a transversal.

Step 1: Set up the equation

The two angles add up to $180^\circ$: $(x + 12) + (x + 48) = 180$

Step 2: Combine like terms

$x + x + 12 + 48 = 180$ $2x + 60 = 180$

Step 3: Solve for $x$

$2x = 180 - 60$ $2x = 120$ $x = 60$

Final Answer:

$x = 60$

Would you like further clarification or a breakdown of any step? Let me know!

Related Questions:

1. What are alternate interior angles, and how do they relate to parallel lines?
2. How can you verify that lines are parallel using angle relationships?
3. What is the difference between supplementary and complementary angles?
4. What other methods exist to prove that two lines are parallel?
5. How does the value of $x$ affect the relationship between lines $A$ and $B$?

Tip:

Always double-check your setup for parallel line problems by confirming which angle relationships are being tested (e.g., supplementary, alternate interior, corresponding).