The complement of the supplement of `138^(@)` is

Options

A. `42^(@)`
B. `48^(@)`
C. `38^(@)`
D. `90^(@)`

Answer

To solve the problem, we need to find the complement of the supplement of 138 degrees. Let's break this down step by step.

### Step 1: Find the Supplement of 138 Degrees
The supplement of an angle is found by subtracting the angle from 180 degrees.

\[ \text{Supplement} = 180^\circ - 138^\circ \]

Calculating this gives:

\[ \text{Supplement} = 180^\circ - 138^\circ = 42^\circ \]

### Step 2: Find the Complement of 42 Degrees
The complement of an angle is found by subtracting the angle from 90 degrees.

\[ \text{Complement} = 90^\circ - 42^\circ \]

Calculating this gives:

\[ \text{Complement} = 90^\circ - 42^\circ = 48^\circ \]

### Final Answer
Thus, the complement of the supplement of 138 degrees is:

\[ \boxed{48^\circ} \]