Find the complement of the angle `(150-a+b)^(@)`

Options

A. `(a-b-60)^@`
B. `(a-b+60)^@`
C. `(a+b+60)^@`
D. `(a+b-60)^@`

Answer

To find the complement of the angle \( (150 - a + b)^\circ \), we can follow these steps:

### Step 1: Understand the concept of complement
The complement of an angle \( x \) is given by the formula:
\[ \text{Complement of } x = 90^\circ - x \]

### Step 2: Define the angle
Let the angle be:
\[ x = 150 - a + b \]

### Step 3: Apply the complement formula
Using the complement formula, we substitute \( x \):
\[ \text{Complement of } (150 - a + b) = 90^\circ - (150 - a + b) \]

### Step 4: Simplify the expression
Now, simplify the expression:
\[ = 90^\circ - 150 + a - b \]
\[ = a - b - 60^\circ \]

### Final Answer
Thus, the complement of the angle \( (150 - a + b)^\circ \) is:
\[ a - b - 60^\circ \]

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