An angle is `32^(@)` less than its supplement. The measure of the angle is

Options

A. `37^(@)`
B. `74^(@)`
C. `148^(@)`
D. none of these

Answer

To find the measure of the angle that is 32 degrees less than its supplement, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem:**
Let the angle be represented as \( x \). The supplement of an angle is calculated as \( 180^\circ - x \).

2. **Setting Up the Equation:**
According to the problem, the angle \( x \) is 32 degrees less than its supplement. Therefore, we can set up the equation:
\[ x = (180^\circ - x) - 32^\circ \]

3. **Simplifying the Equation:**
Rearranging the equation gives:
\[ x = 180^\circ - x - 32^\circ \]
Simplifying further:
\[ x + x = 180^\circ - 32^\circ \]
\[ 2x = 148^\circ \]

4. **Solving for \( x \):**
Now, divide both sides by 2:
\[ x = \frac{148^\circ}{2} = 74^\circ \]

5. **Finding the Supplement:**
To find the supplement of the angle, we can calculate:
\[ 180^\circ - x = 180^\circ - 74^\circ = 106^\circ \]

### Final Result:
The measure of the angle is \( 74^\circ \).