In `DeltaABC, angleA=x+15^(@),angleB=x and angleC=2x-35^(@)` find, each angle of the triangle.

Answer

To find the angles of triangle ABC where angle A = x + 15°, angle B = x°, and angle C = 2x - 35°, we can follow these steps:

### Step-by-step Solution:

1. **Use the Angle Sum Property of a Triangle**:
The sum of the angles in a triangle is always 180°. Therefore, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180° \]
Substituting the expressions for the angles, we have:
\[ (x + 15) + x + (2x - 35) = 180 \]

2. **Combine Like Terms**:
Simplifying the left side of the equation:
\[ x + 15 + x + 2x - 35 = 180 \]
This simplifies to:
\[ 4x - 20 = 180 \]

3. **Isolate x**:
To solve for x, first add 20 to both sides:
\[ 4x = 180 + 20 \]
\[ 4x = 200 \]
Now, divide both sides by 4:
\[ x = \frac{200}{4} = 50 \]

4. **Calculate Each Angle**:
Now that we have the value of x, we can find each angle:
- **Angle A**:
\[ \text{Angle A} = x + 15 = 50 + 15 = 65° \]
- **Angle B**:
\[ \text{Angle B} = x = 50° \]
- **Angle C**:
\[ \text{Angle C} = 2x - 35 = 2(50) - 35 = 100 - 35 = 65° \]

5. **Final Angles**:
Therefore, the angles of triangle ABC are:
- Angle A = 65°
- Angle B = 50°
- Angle C = 65°

### Summary:
- Angle A = 65°
- Angle B = 50°
- Angle C = 65°