https://file.aiquickdraw.com/mathbot/file/1726483407122w4iof7x7.jpg

The image shows a diagram of two intersecting lines, with two marked angles. The two angles are represented by the expressions:

- \( (2x + 48)^\circ \)
- \( (5x + 9)^\circ \)

These angles are **vertically opposite angles**, meaning they are equal. Thus, we can set up the following equation:

\[
2x + 48 = 5x + 9
\]

### Solving the equation:

1. Subtract \(2x\) from both sides to get:
   \[
   48 = 3x + 9
   \]

2. Subtract 9 from both sides:
   \[
   39 = 3x
   \]

3. Divide both sides by 3:
   \[
   x = 13
   \]

### Now, substitute \(x = 13\) back into the expressions for the angles:

- For \( (2x + 48)^\circ \):
  \[
  2(13) + 48 = 26 + 48 = 74^\circ
  \]

- For \( (5x + 9)^\circ \):
  \[
  5(13) + 9 = 65 + 9 = 74^\circ
  \]

Thus, both angles are \(74^\circ\), as expected for vertically opposite angles.

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. What are vertically opposite angles, and why are they always equal?
2. How would you solve this if one of the angles was supplementary to the other?
3. If the angles were supplementary, what would the equation look like?
4. How do we handle angle measurements involving fractions of \(x\)?
5. What are some real-life examples where vertically opposite angles are used?

**Tip:** Vertically opposite angles are always equal when two straight lines intersect. Keep this property in mind for geometry problems involving angles!

Find the measure of each marked angle. (The angles are represented by expressions 2x + 48 and 5x + 9.)

Learn how to solve for vertically opposite angles given by algebraic expressions (2x + 48)° and (5x + 9)°. This problem covers key concepts in algebra and geometry, suitable for students in Grades 7-9.

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