https://file.aiquickdraw.com/mathbot/file/172711130471803l1f2qt.jpg

The problem asks for the measures of two supplementary angles, where the difference between the measures of the two angles is 35°.

### Step-by-Step Solution:

1. **Definition of supplementary angles**: Two angles are supplementary if their measures add up to 180°.

   Let the two angles be \( x \) and \( y \). According to the problem:
   - \( x + y = 180° \)
   - \( |x - y| = 35° \) (the difference between their measures is 35°).

2. **Solve using a system of equations**:
   - From \( x + y = 180° \), we can express \( y \) as \( y = 180° - x \).
   - Now substitute this into the second equation, \( |x - y| = 35° \):
   
     \[
     |x - (180° - x)| = 35°
     \]
     Simplify the absolute value:
     \[
     |2x - 180°| = 35°
     \]
   - Remove the absolute value by considering two cases:
     - \( 2x - 180° = 35° \)
     - \( 2x - 180° = -35° \)

3. **Solve both cases**:
   - Case 1: \( 2x - 180° = 35° \)
     \[
     2x = 215°
     \]
     \[
     x = 107.5°
     \]
     Now, \( y = 180° - 107.5° = 72.5° \).

   - Case 2: \( 2x - 180° = -35° \)
     \[
     2x = 145°
     \]
     \[
     x = 72.5°
     \]
     Now, \( y = 180° - 72.5° = 107.5° \).

In both cases, the two angles are \( 107.5° \) and \( 72.5° \).

### Conclusion:
The correct answer is **B) 72.5°, 107.5°**.

Would you like more details or explanations on any part? Here are five related questions to deepen your understanding:

1. What are complementary angles, and how do they differ from supplementary angles?
2. Can you derive a formula for finding two supplementary angles given their difference?
3. What happens when the difference between supplementary angles is 0°?
4. How do you solve for the measures of angles if the sum is not supplementary but a different total (e.g., 90° or 360°)?
5. How do the concepts of absolute value and inequalities come into play in this problem?

**Tip:** Always remember that supplementary angles sum to 180°, and the difference helps determine how far apart the angles are in size.

Find the measures of two supplementary angles if the difference between the measures of the two angles is 35°.

Learn how to find the measures of two supplementary angles when the difference between them is 35°. This problem uses algebra and geometry, focusing on the properties of supplementary angles and solving a system of equations. 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