The angles of trinalge are in the ratio `2:3:4`. What is the degree measures of the largest angle?

Options

A. `40`
B. `80`
C. `90`
D. `120`

Answer

To find the degree measures of the largest angle in a triangle where the angles are in the ratio of 2:3:4, 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 = 2x
- Angle B = 3x
- Angle C = 4x

2. **Use the Triangle Angle Sum Property:**
The sum of the angles in a triangle is always 180 degrees. Therefore, we can set up the equation:
\[ A + B + C = 180^\circ \]
Substituting the expressions for A, B, and C, we get:
\[ 2x + 3x + 4x = 180^\circ \]

3. **Combine Like Terms:**
Combine the terms on the left side:
\[ 9x = 180^\circ \]

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

5. **Calculate Each Angle:**
Now that we have the value of x, we can find each angle:
- Angle A = 2x = 2(20^\circ) = 40^\circ
- Angle B = 3x = 3(20^\circ) = 60^\circ
- Angle C = 4x = 4(20^\circ) = 80^\circ

6. **Identify the Largest Angle:**
Among the angles calculated, the largest angle is:
\[ \text{Largest Angle} = 80^\circ \]

### Final Answer:
The degree measure of the largest angle in the triangle is **80 degrees**.

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