Two supplementary angles are in the ratio `3:7` Find the difference between the angle.

Explanation

To solve the problem of finding the difference between two supplementary angles that are in the ratio of 3:7, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Supplementary Angles**:
Supplementary angles are two angles whose sum is 180 degrees.

2. **Setting Up the Ratio**:
Let the two angles be represented as \(3x\) and \(7x\) based on the given ratio of 3:7.

3. **Writing the Equation**:
Since these two angles are supplementary, we can write the equation:
\[ 3x + 7x = 180 \]

4. **Combining Like Terms**:
Combine the terms on the left side of the equation:
\[ 10x = 180 \]

5. **Solving for x**:
Divide both sides by 10 to find the value of \(x\):
\[ x = \frac{180}{10} = 18 \]

6. **Finding the Angles**:
Now, substitute \(x\) back into the expressions for the angles:
- First angle:
\[ 3x = 3 \times 18 = 54 \text{ degrees} \]
- Second angle:
\[ 7x = 7 \times 18 = 126 \text{ degrees} \]

7. **Calculating the Difference**:
Finally, find the difference between the two angles:
\[ 126 - 54 = 72 \text{ degrees} \]

### Final Answer:
The difference between the two angles is **72 degrees**.

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