Measures (in degrees) of two supplementary angles are consecutive odd integers. Find the angles.

Answer

To solve the problem of finding two supplementary angles that are consecutive odd integers, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We need to find two angles that are supplementary, meaning their sum is 180 degrees.
- These angles are also consecutive odd integers.

2. **Setting Up the Variables**:
- Let's denote the first angle as \( 2x + 1 \) (the first consecutive odd integer).
- The second angle will then be \( 2x + 3 \) (the next consecutive odd integer).

3. **Writing the Equation**:
- Since the angles are supplementary, we can write the equation:
\[ (2x + 1) + (2x + 3) = 180 \]

4. **Simplifying the Equation**:
- Combine like terms:
\[ 2x + 1 + 2x + 3 = 180 \]
\[ 4x + 4 = 180 \]

5. **Isolating the Variable**:
- Subtract 4 from both sides:
\[ 4x = 180 - 4 \]
\[ 4x = 176 \]
- Now, divide both sides by 4:
\[ x = \frac{176}{4} = 44 \]

6. **Finding the Angles**:
- Now that we have \( x \), we can find the two angles:
- First angle:
\[ 2x + 1 = 2(44) + 1 = 88 + 1 = 89 \text{ degrees} \]
- Second angle:
\[ 2x + 3 = 2(44) + 3 = 88 + 3 = 91 \text{ degrees} \]

7. **Conclusion**:
- The two supplementary angles are \( 89 \) degrees and \( 91 \) degrees.

### Final Answer:
The two supplementary angles that are consecutive odd integers are **89 degrees and 91 degrees**.