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

Explanation

To solve the problem, we need to find the measure of an angle (let's call it α) that is 30 degrees less than its supplement. Here’s how we can approach this step by step:

### Step 1: Define the angle
Let the angle be α (in degrees).

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

### Step 3: Set up the equation
According to the problem, the angle α is 30 degrees less than its supplement. We can express this relationship mathematically as:
\[ α = (180^\circ - α) - 30^\circ \]

### Step 4: Simplify the equation
Now, let's simplify the equation:
1. Start with the equation:
\[ α = 180^\circ - α - 30^\circ \]
2. Combine like terms:
\[ α = 180^\circ - 30^\circ - α \]
\[ α = 150^\circ - α \]

### Step 5: Solve for α
Now, we can add α to both sides of the equation to isolate α:
\[ α + α = 150^\circ \]
\[ 2α = 150^\circ \]

### Step 6: Divide by 2
Now, divide both sides by 2 to find the value of α:
\[ α = \frac{150^\circ}{2} \]
\[ α = 75^\circ \]

### Final Answer
The measure of the angle is:
\[ α = 75^\circ \]

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