The difference between the largest and the smallest angles of a triangle whose angles are in the ratio of 4:3:8 is :

Options

A. A)`30^(@)`
B. B)`50^(@)`
C. C)`40^(@)`
D. D)`60^(@)`

Answer

To solve the problem, we need to find the difference between the largest and the smallest angles of a triangle whose angles are in the ratio of 4:3:8.

### Step-by-Step Solution:

1. **Understand the Ratio of Angles:**
The angles of the triangle are given in the ratio of 4:3:8. We can represent the angles as:
- Angle A = 4x
- Angle B = 3x
- Angle C = 8x

2. **Set Up the Equation:**
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ 4x + 3x + 8x = 180 \]

3. **Combine Like Terms:**
Combine the terms on the left side:
\[ 15x = 180 \]

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

5. **Calculate Each Angle:**
Now that we have the value of x, we can find each angle:
- Angle A = 4x = 4 * 12 = 48 degrees
- Angle B = 3x = 3 * 12 = 36 degrees
- Angle C = 8x = 8 * 12 = 96 degrees

6. **Identify the Largest and Smallest Angles:**
From the calculated angles:
- The largest angle is 96 degrees (Angle C).
- The smallest angle is 36 degrees (Angle B).

7. **Find the Difference:**
Now, we find the difference between the largest and smallest angles:
\[ \text{Difference} = \text{Largest Angle} - \text{Smallest Angle} = 96 - 36 = 60 \text{ degrees} \]

### Final Answer:
The difference between the largest and the smallest angles of the triangle is **60 degrees**.