Find the angle of a triangle which are in the ratio `3:4:5`.

Answer

To find the angles of a triangle that are in the ratio of 3:4:5, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Angles in Terms of a Variable**:
Let the angles of the triangle be represented as:
- Angle A = 3x
- Angle B = 4x
- Angle C = 5x

2. **Use the Property of Triangles**:
We know that the sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
Substituting the expressions for the angles, we get:
\[ 3x + 4x + 5x = 180^\circ \]

3. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ (3x + 4x + 5x) = 12x \]
So, we have:
\[ 12x = 180^\circ \]

4. **Solve for x**:
To find the value of x, divide both sides of the equation by 12:
\[ x = \frac{180^\circ}{12} = 15^\circ \]

5. **Calculate Each Angle**:
Now that we have the value of x, we can find each angle:
- Angle A = 3x = 3 * 15 = 45 degrees
- Angle B = 4x = 4 * 15 = 60 degrees
- Angle C = 5x = 5 * 15 = 75 degrees

6. **Conclusion**:
The angles of the triangle are:
- Angle A = 45 degrees
- Angle B = 60 degrees
- Angle C = 75 degrees