https://file.aiquickdraw.com/mathbot/file/17259822323229zorcw70.jpg

The problem involves solving for \( x \) using the relationship between the given angles. The angles provided in the diagram appear to be vertical angles because they are opposite each other when two lines intersect. Vertical angles are always equal.

### Given:
- One angle is labeled as \( (4x - 7)^\circ \).
- The other angle is labeled as \( (7x - 61)^\circ \).

### Since the angles are vertical angles, we can set them equal:
\[
4x - 7 = 7x - 61
\]

### Now, solve for \( x \):

1. Subtract \( 4x \) from both sides:
\[
-7 = 3x - 61
\]

2. Add 61 to both sides:
\[
54 = 3x
\]

3. Divide by 3:
\[
x = 18
\]

### So, the value of \( x \) is \( \boxed{18} \).

Would you like further details on this solution or have any other questions?

Here are 5 related questions to practice:
1. If the angles were supplementary, how would you solve for \( x \)?
2. What would be the angle measures if \( x = 18 \)?
3. How do you determine if two angles are supplementary or vertical?
4. What happens to the value of \( x \) if the expression on the right side were \( (7x + 61)^\circ \)?
5. How would you check your answer to ensure it is correct?

**Tip:** When dealing with angle relationships, always consider if they are vertical, supplementary, or complementary as this will dictate the equation to solve.

Solve for x using the relationship between the angles labeled as (4x - 7)° and (7x - 61)°. The angles are opposite each other and therefore equal.

Learn how to solve for x by using the vertical angles theorem where two angles are equal. This step-by-step guide walks you through solving the equation 4x - 7 = 7x - 61. Perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation