https://file.aiquickdraw.com/mathbot/file/17254033730525go7mi2j.jpg

The figure shows two intersecting lines forming vertical angles. One angle is given as \(63^\circ\), and the vertically opposite angle is represented as \((1.5x + 18)^\circ\).

### Solution:
Vertical angles are congruent, meaning they have equal measures. Therefore, we can set up the equation:

\[
63 = 1.5x + 18
\]

#### Solving for \(x\):

1. Subtract 18 from both sides:

\[
63 - 18 = 1.5x
\]

\[
45 = 1.5x
\]

2. Divide both sides by 1.5:

\[
x = \frac{45}{1.5}
\]

\[
x = 30
\]

### Conclusion:
The value of \(x\) is \(30\).

Would you like more details, or do you have any questions?

Here are five related questions to expand on this topic:
1. What are supplementary angles, and how are they different from vertical angles?
2. How would you solve for \(x\) if the angles were supplementary instead?
3. What other properties of angles can be found in intersecting lines?
4. How can you use the properties of angles to solve problems involving polygons?
5. How do angle bisectors affect the measures of angles in a triangle?

**Tip:** Always remember that vertical angles are equal, and this property is helpful for solving many geometry problems!

Use the figure to find the value of x, where one angle is given as 63° and the vertically opposite angle is represented as (1.5x + 18)°.

Learn how to solve for x in the problem where two vertically opposite angles are given as 63° and (1.5x + 18)°. Understand the use of the Vertical Angles Theorem and basic algebra to find the solution. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation