The angles of a triangle are in the ratio of 2:3:4, the measurement of greatest angle is-

Options

A. `30^(@)`
B. `60^(@)`
C. `100^(@)`
D. `80^(@)`

Answer

To find the measurement of the greatest angle in a triangle where the angles are in the ratio of 2:3:4, we can follow these steps:

### Step 1: Assign Variables
Let the angles of the triangle be represented as:
- First angle = 2x
- Second angle = 3x
- Third angle = 4x

### Step 2: Set Up the Equation
According to the properties of triangles, the sum of the internal angles of a triangle is always 180 degrees. Therefore, we can set up the equation:
\[ 2x + 3x + 4x = 180 \]

### Step 3: Combine Like Terms
Combine the terms on the left side of the equation:
\[ (2x + 3x + 4x) = 9x \]
So, the equation becomes:
\[ 9x = 180 \]

### Step 4: Solve for x
To find the value of x, divide both sides of the equation by 9:
\[ x = \frac{180}{9} \]
\[ x = 20 \]

### Step 5: Calculate Each Angle
Now that we have the value of x, we can find each angle:
- First angle = \( 2x = 2 \times 20 = 40 \) degrees
- Second angle = \( 3x = 3 \times 20 = 60 \) degrees
- Third angle = \( 4x = 4 \times 20 = 80 \) degrees

### Step 6: Identify the Greatest Angle
From the calculated angles, we can see that the greatest angle is:
\[ 80 \text{ degrees} \]

### Final Answer
Thus, the measurement of the greatest angle in the triangle is **80 degrees**.

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