In a triangles ABC `, angle A = x^(@) , angle B = (3x - 2) ^(@) and angle C = y^(@) , " Also " ,angle C - angle B = 9^(@) ` Find all the three angles of the ` Delta ABC `.

Answer

To find the angles of triangle ABC, we will follow these steps:

### Step 1: Set up the equations based on the given information.
We know:
- Angle A = x degrees
- Angle B = (3x - 2) degrees
- Angle C = y degrees
- The sum of angles in a triangle is 180 degrees:
\[ A + B + C = 180 \]
Therefore, we can write:
\[ x + (3x - 2) + y = 180 \quad \text{(Equation 1)} \]

### Step 2: Use the second condition provided.
We are also given that:
- Angle C - Angle B = 9 degrees:
\[ y - (3x - 2) = 9 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2.
From Equation 2:
\[ y - 3x + 2 = 9 \]
Rearranging gives:
\[ y = 3x + 7 \quad \text{(Equation 3)} \]

### Step 4: Substitute Equation 3 into Equation 1.
Now, substitute the value of y from Equation 3 into Equation 1:
\[ x + (3x - 2) + (3x + 7) = 180 \]
This simplifies to:
\[ x + 3x - 2 + 3x + 7 = 180 \]
Combining like terms:
\[ 7x + 5 = 180 \]

### Step 5: Solve for x.
Subtract 5 from both sides:
\[ 7x = 175 \]
Now divide by 7:
\[ x = 25 \]

### Step 6: Find y using x.
Now substitute x back into Equation 3 to find y:
\[ y = 3(25) + 7 = 75 + 7 = 82 \]

### Step 7: Find Angle B using x.
Now calculate Angle B:
\[ B = 3x - 2 = 3(25) - 2 = 75 - 2 = 73 \]

### Step 8: Summarize the angles.
Now we have:
- Angle A = x = 25 degrees
- Angle B = 73 degrees
- Angle C = y = 82 degrees

### Final Answer:
Thus, the angles of triangle ABC are:
- Angle A = 25°
- Angle B = 73°
- Angle C = 82°

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