Given that `angleA` and `angleB` are supplementary angles. If `angleA:angleB=7:8`, 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 and their ratio is 7:8.

### Step-by-Step Solution:

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

2. **Setting Up the Ratio**:
- Given the ratio of angle A to angle B is 7:8, we can express angle A and angle B in terms of a variable \( x \):
\[ \text{angle A} = 7x \quad \text{and} \quad \text{angle B} = 8x \]

3. **Substituting into the Equation**:
- Now substitute the expressions for angle A and angle B into the supplementary angle equation:
\[ 7x + 8x = 180^\circ \]

4. **Combining Like Terms**:
- Combine the terms on the left side:
\[ 15x = 180^\circ \]

5. **Solving for \( x \)**:
- To find the value of \( x \), divide both sides by 15:
\[ x = \frac{180}{15} = 12 \]

6. **Finding Angle A and Angle B**:
- Now that we have \( x \), we can find the measures of angle A and angle B:
- For angle A:
\[ \text{angle A} = 7x = 7 \times 12 = 84^\circ \]
- For angle B:
\[ \text{angle B} = 8x = 8 \times 12 = 96^\circ \]

7. **Final Answer**:
- Therefore, the measures of the angles are:
\[ \text{angle A} = 84^\circ \quad \text{and} \quad \text{angle B} = 96^\circ \]