In the image provided, we are asked to find the value of $x$. The diagram shows two intersecting lines, forming angles $(2x + 4)^\circ$ and $140^\circ$.

Solution:

The angles formed are supplementary because they are on the same side of a straight line. This means that their sum is $180^\circ$.

Therefore, we can set up the equation:

$(2x + 4)^\circ + 140^\circ = 180^\circ$

Now, solve for $x$:

$2x + 4 + 140 = 180$

Simplify:

$2x + 144 = 180$

Subtract 144 from both sides:

$2x = 36$

Now, divide by 2:

$x = 18$

So, the value of $x$ is $18$.

Would you like a further breakdown, or do you have any questions?

Here are 5 related questions for practice:

1. What is the relationship between vertically opposite angles?
2. If the angle was $(3x + 10)^\circ$ instead of $(2x + 4)^\circ$, how would you solve it?
3. Can two angles be supplementary if both are acute angles? Why or why not?
4. If two angles add up to $90^\circ$, what are they called?
5. How would you solve for $x$ if the two angles were complementary instead?

Tip: Always check if angles are supplementary or complementary based on their positions before setting up your equation.