If one of the angles of a triangle is greater than each of the two remaining angles by `30^(@)` , then the angles of the triangle are

Options

A. `40^(@), 40^(@), 100^(@)`
B. `50^(@), 50^(@), 80^(@)`
C. `30^(@), 30^(@), 120^(@)`
D. `35^(@), 35^(@), 110^(@)`

Answer

To solve the problem, we need to find the angles of a triangle given that one angle is greater than each of the other two angles by 30 degrees. Let's break this down step by step.

### Step-by-Step Solution:

1. **Define the Angles**:
Let the two smaller angles of the triangle be \( x \) degrees each. According to the problem, the greater angle will then be \( x + 30 \) degrees.

2. **Set Up the Equation**:
The sum of the angles in a triangle is always \( 180 \) degrees. Therefore, we can write the equation:
\[ x + x + (x + 30) = 180 \]

3. **Simplify the Equation**:
Combine like terms in the equation:
\[ 3x + 30 = 180 \]

4. **Isolate \( x \)**:
Subtract \( 30 \) from both sides to isolate the terms with \( x \):
\[ 3x = 180 - 30 \]
\[ 3x = 150 \]

5. **Solve for \( x \)**:
Divide both sides by \( 3 \) to find \( x \):
\[ x = \frac{150}{3} = 50 \]

6. **Find the Angles**:
Now that we have \( x \), we can find the angles of the triangle:
- The two smaller angles are \( 50 \) degrees each.
- The greater angle is \( x + 30 = 50 + 30 = 80 \) degrees.

7. **List the Angles**:
Therefore, the angles of the triangle are:
- \( 50 \) degrees
- \( 50 \) degrees
- \( 80 \) degrees

### Final Answer:
The angles of the triangle are \( 50^\circ, 50^\circ, \) and \( 80^\circ \).

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