https://file.aiquickdraw.com/mathbot/file/17268509982660xh7yksj.jpg

In the image, you have two intersecting lines with angles marked as \( 50^\circ \), \( x^\circ \), and \( y^\circ \). These form vertical angles and supplementary angles.

### Solving for \( x \):
- The angles \( 50^\circ \) and \( x^\circ \) are vertically opposite angles. 
- Vertically opposite angles are always equal.
  
Thus, \( x = 50^\circ \).

### Solving for \( y \):
- Angles \( x^\circ \) and \( y^\circ \) form a straight line, meaning they are supplementary. 
- Supplementary angles sum to \( 180^\circ \).

Since \( x = 50^\circ \), we can write the equation:

\[
y + 50 = 180
\]

Solving for \( y \):

\[
y = 180 - 50 = 130^\circ
\]

### Answers:
- \( x = 50^\circ \)
- \( y = 130^\circ \)

Would you like further details or have any questions? Here are five related questions to expand on this concept:

1. What are the properties of vertically opposite angles?
2. How can you determine the measure of an unknown angle in a triangle?
3. What is the relationship between complementary and supplementary angles?
4. Can two acute angles be supplementary? Why or why not?
5. How are corresponding angles used to solve for unknown angles in parallel lines?

**Tip:** Always look for vertical or supplementary angle relationships when dealing with intersecting lines!

Use the diagram to answer the following questions. Solve for x and y based on the given angles.

This problem involves solving for x and y using the properties of vertically opposite angles and supplementary angles. Vertically opposite angles are equal, and supplementary angles sum to 180 degrees. 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