Two supplementary angles are in the ratio `7: 8`. Find the angles

Answer

To solve the problem of finding two supplementary angles that are in the ratio of 7:8, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Supplementary Angles**:
- Supplementary angles are two angles whose sum is 180 degrees.

2. **Set Up the Variables**:
- Let the first angle be \( x \) degrees.
- Since the angles are supplementary, the second angle will be \( 180 - x \) degrees.

3. **Set Up the Ratio**:
- According to the problem, the ratio of the two angles is \( 7:8 \).
- This can be expressed as:
\[ \frac{x}{180 - x} = \frac{7}{8} \]

4. **Cross Multiply to Solve for \( x \)**:
- Cross multiplying gives us:
\[ 8x = 7(180 - x) \]

5. **Distribute and Rearrange the Equation**:
- Distributing the 7 on the right side:
\[ 8x = 1260 - 7x \]
- Now, add \( 7x \) to both sides:
\[ 8x + 7x = 1260 \]
\[ 15x = 1260 \]

6. **Solve for \( x \)**:
- Divide both sides by 15:
\[ x = \frac{1260}{15} = 84 \]

7. **Find the Second Angle**:
- Now that we have \( x = 84 \) degrees, we can find the second angle:
\[ 180 - x = 180 - 84 = 96 \]

8. **Conclusion**:
- The two angles are \( 84 \) degrees and \( 96 \) degrees.

### Final Answer:
The two supplementary angles are \( 84 \) degrees and \( 96 \) degrees.

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