https://file.aiquickdraw.com/mathbot/file/1726196325978yvv1pq4o.jpg

The given image shows two intersecting lines forming vertical angles. The angles are labeled as:

- \( (5r + 8)^\circ \)
- \( (7r - 8)^\circ \)

### Vertical Angles:
Vertical angles are equal when two lines intersect. This gives us the equation:

\[
5r + 8 = 7r - 8
\]

### Solving for \( r \):

1. Subtract \( 5r \) from both sides:

\[
8 = 2r - 8
\]

2. Add 8 to both sides:

\[
16 = 2r
\]

3. Divide by 2:

\[
r = 8
\]

Thus, the value of \( r \) is **8**.

Would you like more details on solving similar problems, or any clarifications?

Here are some related questions to expand on this concept:
1. What are the properties of vertical angles?
2. How would the equation change if the angles were complementary?
3. Can vertical angles be obtuse or acute, and how would that affect the solution?
4. How do you solve equations involving unknowns in multiple angles at an intersection?
5. What are some real-world applications of solving vertical angles?

**Tip:** Always check if angles are complementary, supplementary, or vertical when solving for unknowns in geometric figures.

Solve for the value of r given the angles (5r + 8)° and (7r - 8)° formed by two intersecting lines.

Discover how to solve for the variable r using vertical angles formed by two intersecting lines. This problem includes algebraic and geometric concepts suitable for students in 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