Complete the statements about the relationship between the two labeled angles.
Given: The labeled angles form a right angle.
The following sentence or sentences contain missing information in the form of one or more blanks. For each blank, there will exist a corresponding input field. Use the input fields to complete the sentence or sentences.
The two labeled angles are Correct Answer.

The following sentence or sentences contain missing information in the form of one or more blanks. For each blank, there will exist a corresponding input field. Use the input fields to complete the sentence or sentences.
That means that their measures Correct Answer.

Use the relationship you determined to write an equation to help you solve for ecks.
Correct Answer
Select the angle labeled with a variable expression. Use the value you calculated for ecks to determine its measure.

Let’s break this problem into steps and fill in the blanks with appropriate reasoning and mathematical principles:

1. **The two labeled angles are**:
   **Complementary** (because they form a right angle, meaning their measures sum to 90 degrees).

2. **That means that their measures**:
   **add up to 90 degrees**.

3. **Write an equation to solve for x**:
   Suppose the two angles are labeled \( x \) and \( y \), and you are given expressions for them (e.g., \( x + 3 \) and \( 2x - 5 \)). Since they are complementary:
   \[
   \text{Angle 1} + \text{Angle 2} = 90
   \]
   Insert the given expressions into this equation to solve for \( x \).

4. **Determine the measure of the angle labeled with a variable expression**:
   Once you calculate \( x \), substitute it back into the expression for the angle(s) to find their specific measures.

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### Example Application:
If the labeled angles are \( x + 3 \) and \( 2x - 5 \), the equation would be:
\[
(x + 3) + (2x - 5) = 90
\]
Simplify:
\[
3x - 2 = 90 \implies 3x = 92 \implies x = \frac{92}{3} \text{ or approximately } 30.67.
\]

Substitute \( x \) back into each expression to find the angles' measures:
\[
\text{Angle 1: } x + 3 = \frac{92}{3} + 3 = \frac{101}{3}.
\]
\[
\text{Angle 2: } 2x - 5 = 2\left(\frac{92}{3}\right) - 5 = \frac{179}{3}.
\]

Would you like a step-by-step example with specific values?  
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### Follow-up Questions:
1. What does it mean for two angles to be complementary?  
2. How do you verify the sum of two complementary angles?  
3. How can algebraic expressions represent angle measures?  
4. What is the role of substitution when solving for unknown variables in equations?  
5. How can the equation setup change if the angles were supplementary instead?

**Tip**: Always double-check that your solution satisfies the original condition (e.g., the sum of complementary angles is 90°).

Complete the statements about the relationship between the two labeled angles. Given: The labeled angles form a right angle. The following sentence or sentences contain missing information in the form of one or more blanks. For each blank, there will exist a corresponding input field. Use the input fields to complete the sentence or sentences. The two labeled angles are Correct Answer. That means that their measures Correct Answer. Use the relationship you determined to write an equation to help you solve for x. Select the angle labeled with a variable expression. Use the value you calculated for x to determine its measure.

Understand the relationship between two complementary angles forming a right angle and solve for unknown angle measures. This problem includes applying algebraic equations to complementary angles and calculating unknown variables. Suitable for students in Grades 6-8.

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