The measure of an angle is `30^(@)` less than its supplement. Find the measure of the angle

Options

A. `180^(@)`
B. `150^(@)`
C. `75^(@)`
D. `105^(@)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the angle
Let the angle be represented as \( x \) degrees.

### Step 2: Write the expression for the supplement
The supplement of the angle \( x \) is given by the formula:
\[ \text{Supplement} = 180^\circ - x \]

### Step 3: Set up the equation based on the problem statement
According to the problem, the angle \( x \) is 30 degrees less than its supplement. This can be expressed mathematically as:
\[ x = (180^\circ - x) - 30^\circ \]

### Step 4: Simplify the equation
Now, we will simplify the equation:
\[ x = 180^\circ - x - 30^\circ \]
\[ x = 150^\circ - x \]

### Step 5: Combine like terms
Next, we will add \( x \) to both sides to combine the terms:
\[ x + x = 150^\circ \]
\[ 2x = 150^\circ \]

### Step 6: Solve for \( x \)
Now, we will divide both sides by 2 to find the value of \( x \):
\[ x = \frac{150^\circ}{2} = 75^\circ \]

### Final Answer
The measure of the angle is \( 75^\circ \).

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