https://file.aiquickdraw.com/mathbot/file/1727197897874c3wgn9w7.jpg

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?

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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.

Find x given the angles (2x + 4)° and 140° in the diagram. The angles are supplementary.

Solve for x given two supplementary angles (2x + 4)° and 140°. This problem involves the use of basic algebra and geometry principles, suitable for students in Grades 6-8. A detailed step-by-step solution is provided to find the value of x.

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