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The problem involves two intersecting lines that form a pair of vertically opposite angles, which are always equal. The angles given are \( 123^\circ \) and \( (2v + 1)^\circ \).

Since these are vertically opposite angles, we can set them equal to each other:

\[
123^\circ = (2v + 1)^\circ
\]

Now, solve for \( v \).

### Step 1: Set up the equation
\[
123 = 2v + 1
\]

### Step 2: Subtract 1 from both sides
\[
122 = 2v
\]

### Step 3: Divide both sides by 2
\[
v = \frac{122}{2} = 61
\]

Thus, the value of \( v \) is:

\[
v = 61
\]

Let me know if you would like further details!

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Here are some related questions you might explore:

1. What is the sum of angles around a point?
2. How do we determine the value of supplementary angles?
3. What are alternate interior angles, and how do they relate to parallel lines?
4. How would the answer change if the given angle was a different value?
5. Can you apply this concept to other geometric configurations?

**Tip:** Always check whether angles are complementary, supplementary, or vertically opposite in geometry problems.

Learn how to solve for the variable v using vertically opposite angles in this geometry problem. The angles given are 123° and (2v + 1)°. Follow step-by-step to find that v = 61. Suitable for students in Grades 6-8.

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