https://file.aiquickdraw.com/mathbot/file/17285810416256ulnmuzc.jpg

In the image, you have two intersecting lines forming vertical angles, labeled as \( (5x + 4)^\circ \) and \( (8x - 71)^\circ \). Vertical angles are always equal, so we can set up the equation:

\[
5x + 4 = 8x - 71
\]

### Solving the equation:

1. First, subtract \(5x\) from both sides to get the \(x\)-terms on one side:

\[
4 = 8x - 5x - 71
\]

2. Simplify the equation:

\[
4 = 3x - 71
\]

3. Add \(71\) to both sides to isolate the \(x\)-term:

\[
4 + 71 = 3x
\]

\[
75 = 3x
\]

4. Finally, divide both sides by \(3\) to solve for \(x\):

\[
x = \frac{75}{3} = 25
\]

Thus, the value of \(x\) is \( \boxed{25} \).

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions to explore:

1. What are vertical angles and why are they always equal?
2. How would you solve this problem if different angles were given?
3. Can this method be applied to non-vertical angles?
4. How would the equation change if one of the angles had a constant instead of an expression with \(x\)?
5. What other angle pairs in intersecting lines follow similar properties?

**Tip**: Always remember that vertical angles are congruent, meaning they are equal in measure!

Find the value of x in the equation (5x + 4)° = (8x - 71)°, where the angles are vertical.

Learn how to solve the linear equation (5x + 4)° = (8x - 71)° by using the Vertical Angle Theorem. This step-by-step solution explains key concepts such as solving for x and understanding vertical angles. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation