https://file.aiquickdraw.com/mathbot/file/1726813141385j5fh3ojq.jpg

The image shows two intersecting lines forming vertical angles. One angle is given as \( 118^\circ \), and the other is expressed as \( (6x + 4)^\circ \). Since these two angles are vertical angles, they are congruent, meaning their measures are equal.

We can set up the equation:
\[
118 = 6x + 4
\]

Now, solving for \( x \):

1. Subtract 4 from both sides:
\[
118 - 4 = 6x
\]
\[
114 = 6x
\]

2. Divide both sides by 6:
\[
x = \frac{114}{6} = 19
\]

So, the value of \( x \) is \( \boxed{19} \).

Would you like more details on the steps, or do you have any further questions?

Here are 5 related questions for practice:
1. If one angle is \( 120^\circ \) and the other is \( (5x + 10)^\circ \), what is the value of \( x \)?
2. What are the properties of vertical angles?
3. How do you solve for \( x \) in an equation where the angles are supplementary?
4. What is the difference between complementary and supplementary angles?
5. How can you solve for \( x \) if the angle is expressed in terms of a linear equation?

**Tip:** Remember that vertical angles are always equal, while supplementary angles add up to 180°.

Find the value of x in the equation formed by two intersecting lines, where one angle is 118° and the other is expressed as (6x + 4)°.

This problem demonstrates how to solve for x using the Vertical Angles Theorem. Two intersecting lines form one angle of 118° and another of (6x + 4)°. By setting the angles equal, we find the value of x. 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