Two supplementary angles are in the ratio 3:2. The smaller angle measures

Options

A. `108^(@)`
B. `81^(@)`
C. `72^(@)`
D. none of these

Answer

To solve the problem of finding the smaller angle when two supplementary angles are in the ratio of 3:2, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We know that supplementary angles are two angles whose sum is 180 degrees. The angles are in the ratio of 3:2.

2. **Assign Variables**: Let the first angle be \(3x\) and the second angle be \(2x\). Here, \(x\) is a common multiplier.

3. **Set Up the Equation**: Since these two angles are supplementary, we can write the equation:
\[ 3x + 2x = 180 \]

4. **Combine Like Terms**: Simplify the left side of the equation:
\[ 5x = 180 \]

5. **Solve for \(x\)**: To find the value of \(x\), divide both sides by 5:
\[ x = \frac{180}{5} = 36 \]

6. **Find the Angles**: Now, substitute \(x\) back into the expressions for the angles:
- First angle:
\[ 3x = 3 \times 36 = 108 \text{ degrees} \]
- Second angle:
\[ 2x = 2 \times 36 = 72 \text{ degrees} \]

7. **Identify the Smaller Angle**: The smaller angle between the two is:
\[ 72 \text{ degrees} \]

### Final Answer:
The measurement of the smaller angle is **72 degrees**.