Given that `angleA` and `angleB` are complementary angles. If `angleA=angleB+20^(@)`, 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 complementary angles and that angle A is 20 degrees more than angle B.

### Step-by-Step Solution:

1. **Understanding Complementary Angles**:
Since angle A and angle B are complementary, we know that:
\[ \text{angle A} + \text{angle B} = 90^\circ \]

2. **Setting Up the Equation**:
We are also given that:
\[ \text{angle A} = \text{angle B} + 20^\circ \]
We can substitute this expression for angle A into the complementary angle equation.

3. **Substituting in the Equation**:
Replace angle A in the first equation:
\[ (\text{angle B} + 20^\circ) + \text{angle B} = 90^\circ \]

4. **Combining Like Terms**:
Combine the terms:
\[ 2 \cdot \text{angle B} + 20^\circ = 90^\circ \]

5. **Isolating angle B**:
Subtract 20 degrees from both sides:
\[ 2 \cdot \text{angle B} = 90^\circ - 20^\circ \]
\[ 2 \cdot \text{angle B} = 70^\circ \]

6. **Dividing to Find angle B**:
Divide both sides by 2:
\[ \text{angle B} = \frac{70^\circ}{2} = 35^\circ \]

7. **Finding angle A**:
Now that we have angle B, we can find angle A using the relation:
\[ \text{angle A} = \text{angle B} + 20^\circ = 35^\circ + 20^\circ = 55^\circ \]

8. **Final Answers**:
Therefore, the measures of the angles are:
\[ \text{angle A} = 55^\circ \quad \text{and} \quad \text{angle B} = 35^\circ \]

### Summary of the Solution:
- Angle A = 55 degrees
- Angle B = 35 degrees