https://file.aiquickdraw.com/mathbot/file/172679122307334320liw.jpg

The image shows a pair of vertical angles with one angle labeled as \( 60^\circ \) and the other angle labeled as \( (9v + 3)^\circ \). The equation provided is \( 9v + 3 = 60 \). Since vertical angles are always equal, we can directly set up the equation to solve for \( v \).

### Solving the equation:

\[
9v + 3 = 60
\]

1. Subtract 3 from both sides:

\[
9v = 60 - 3
\]
\[
9v = 57
\]

2. Divide both sides by 9:

\[
v = \frac{57}{9}
\]
\[
v = 6.33 \ (\text{rounded to two decimal places})
\]

Thus, the value of \( v \) is approximately \( 6.33 \).

Would you like further details or have any questions?

Here are 5 related questions to extend your understanding:
1. What are vertical angles, and why are they always equal?
2. How can we verify the solution by substituting \( v \) back into the original equation?
3. What happens if you have more complex expressions for both vertical angles?
4. How would this problem change if the angles formed were complementary instead of vertical?
5. Can vertical angles be acute, obtuse, or right angles? Explain your reasoning.

**Tip:** When solving for variables in angle relationships, always verify if the angles are vertical, complementary, or supplementary to apply the correct equations.

Solve for the value of v in the equation 9v + 3 = 60, given that vertical angles are equal with one angle being 60° and the other (9v + 3)°.

Learn how to solve for v in the equation 9v + 3 = 60 by applying the Vertical Angles Theorem, where one angle is 60°. This step-by-step solution covers algebraic manipulation and geometric concepts, ideal for students in Grades 7-9.

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