The larger of the two supplementary angles exceeds the smaller by `20^(@)`. Find smaller angle.

Options

A. `80^(@)`
B. `100^(@)`
C. `90^(@)`
D. `70^(@)`

Answer

To solve the problem of finding the smaller angle when the larger of two supplementary angles exceeds the smaller by \(20^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables:**
Let the smaller angle be \(x\).

2. **Express the Larger Angle:**
Since the larger angle exceeds the smaller angle by \(20^\circ\), we can express the larger angle as:
\[ \text{Larger angle} = x + 20^\circ \]

3. **Set Up the Equation:**
Since the two angles are supplementary, their sum is equal to \(180^\circ\). Therefore, we can write the equation:
\[ x + (x + 20) = 180 \]

4. **Simplify the Equation:**
Combine like terms in the equation:
\[ 2x + 20 = 180 \]

5. **Isolate the Variable:**
Subtract \(20\) from both sides to isolate the term with \(x\):
\[ 2x = 180 - 20 \]
\[ 2x = 160 \]

6. **Solve for \(x\):**
Divide both sides by \(2\) to find the value of \(x\):
\[ x = \frac{160}{2} \]
\[ x = 80 \]

7. **Conclusion:**
The smaller angle is \(80^\circ\).

### Final Answer:
The smaller angle is \(80^\circ\).