If the angle of a triangle are in the ratio of 2:5:8, then find the value of the smallest angle.

A. `36^(@)`

B. `18^(@)`

C. `12^(@)`

D. `24^(@)`

Options

A. A
B. D
C. B
D. C

Answer

To find the smallest angle of a triangle whose angles are in the ratio of 2:5:8, we can follow these steps:

### Step 1: Assign Variables
Let the angles of the triangle be represented as:
- Angle A = 2x
- Angle B = 5x
- Angle C = 8x

### Step 2: Set Up the Equation
The sum of the angles in a triangle is always 180 degrees. Therefore, we can set up the equation:
\[ 2x + 5x + 8x = 180 \]

### Step 3: Combine Like Terms
Combine the terms on the left side of the equation:
\[ 15x = 180 \]

### Step 4: Solve for x
Now, divide both sides by 15 to find the value of x:
\[ x = \frac{180}{15} \]
\[ x = 12 \]

### Step 5: Calculate Each Angle
Now we can find the measures of each angle:
- Angle A = 2x = 2(12) = 24 degrees
- Angle B = 5x = 5(12) = 60 degrees
- Angle C = 8x = 8(12) = 96 degrees

### Step 6: Identify the Smallest Angle
From the calculated angles, the smallest angle is:
- Angle A = 24 degrees

Thus, the smallest angle is **24 degrees**.

### Final Answer
The value of the smallest angle is **24 degrees** (Option D).

---