If `angleA` and `angleB` are supplementary angles, where `angleA=x+10^(@)` and `angleB=x-10^(@)`, then find `angleA` and `angleB`.

Answer

To solve the problem, we need to find the measures of angles A and B, given that they are supplementary angles.

### Step-by-Step Solution:

1. **Understanding Supplementary Angles**:
- By definition, two angles are supplementary if their sum is equal to 180 degrees.
- Therefore, we can write the equation:
\[ \text{angle A} + \text{angle B} = 180^\circ \]

2. **Substituting the Given Expressions**:
- We know that:
\[ \text{angle A} = x + 10^\circ \]
\[ \text{angle B} = x - 10^\circ \]
- Substituting these into the equation gives:
\[ (x + 10) + (x - 10) = 180 \]

3. **Simplifying the Equation**:
- Combine like terms:
\[ x + 10 + x - 10 = 180 \]
\[ 2x = 180 \]

4. **Solving for x**:
- Divide both sides by 2:
\[ x = \frac{180}{2} = 90 \]

5. **Finding Angle A**:
- Substitute \( x \) back into the expression for angle A:
\[ \text{angle A} = x + 10 = 90 + 10 = 100^\circ \]

6. **Finding Angle B**:
- Substitute \( x \) back into the expression for angle B:
\[ \text{angle B} = x - 10 = 90 - 10 = 80^\circ \]

### Final Answer:
- Therefore, the measures of the angles are:
- **Angle A = 100 degrees**
- **Angle B = 80 degrees**