The larger of two supplementary angles exceeds the smaller by `18^(@)` . Find the angles .

Answer

To solve the problem of finding two supplementary angles where the larger angle exceeds the smaller by \(18^\circ\), we can follow these steps:

### Step-by-step Solution:

1. **Define the Variables**:
Let the smaller angle be \(x\) degrees. Since the larger angle exceeds the smaller angle by \(18^\circ\), we can express the larger angle as:
\[ \text{Larger angle} = x + 18 \]

2. **Use the Property of Supplementary Angles**:
By definition, supplementary angles add up to \(180^\circ\). Therefore, we can write the equation:
\[ x + (x + 18) = 180 \]

3. **Simplify the Equation**:
Combine like terms in the equation:
\[ 2x + 18 = 180 \]

4. **Isolate the Variable**:
To solve for \(x\), first subtract \(18\) from both sides:
\[ 2x = 180 - 18 \]
\[ 2x = 162 \]

5. **Solve for \(x\)**:
Divide both sides by \(2\):
\[ x = \frac{162}{2} = 81 \]

6. **Find the Larger Angle**:
Now that we have the smaller angle, we can find the larger angle:
\[ \text{Larger angle} = x + 18 = 81 + 18 = 99 \]

### Conclusion:
The two supplementary angles are:
- Smaller angle: \(81^\circ\)
- Larger angle: \(99^\circ\)