If an angle is `60^(@)` less than two times of its supplement, then the greater angle is

Options

A. `100^(@)`
B. `80^(@)`
C. `60^(@)`
D. `120^(@)`

Answer

To solve the problem, we need to find an angle that is 60 degrees less than twice its supplement. Let's break it down step by step.

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

### Step 2: Define the supplement of the angle
The supplement of the angle \( \theta \) is given by:
\[ 180 - \theta \]

### Step 3: Set up the equation
According to the problem, the angle \( \theta \) is 60 degrees less than twice its supplement. Therefore, we can write the equation as:
\[ \theta = 2(180 - \theta) - 60 \]

### Step 4: Simplify the equation
Now, let's simplify the equation:
\[ \theta = 2(180) - 2\theta - 60 \]
\[ \theta = 360 - 2\theta - 60 \]
\[ \theta + 2\theta = 360 - 60 \]
\[ 3\theta = 300 \]

### Step 5: Solve for \( \theta \)
Now, divide both sides by 3 to find \( \theta \):
\[ \theta = \frac{300}{3} = 100 \]

### Step 6: Find the supplement angle
Now that we have \( \theta \), we can find its supplement:
\[ \text{Supplement} = 180 - \theta = 180 - 100 = 80 \]

### Step 7: Determine the greater angle
Now we have two angles: \( \theta = 100 \) degrees and its supplement = 80 degrees. The greater angle is:
\[ \text{Greater angle} = 100 \text{ degrees} \]

### Final Answer
The greater angle is \( 100 \) degrees.

---