In triangles ABC, the measures of angles a, b, and c, respectively, are in the ratio 2:3:4.What is the measure of angle b?

Options

A. `20`
B. `40`
C. `60`
D. `80`

Answer

To solve the problem, we need to find the measure of angle B in triangle ABC, where the angles are in the ratio 2:3:4.

### Step-by-Step Solution:

1. **Understand the properties of triangles**:
The sum of the angles in any triangle is always 180 degrees.

2. **Set up the ratio**:
Given the angles A, B, and C are in the ratio 2:3:4, we can express them in terms of a variable \( x \):
- Let angle A = \( 2x \)
- Let angle B = \( 3x \)
- Let angle C = \( 4x \)

3. **Write the equation for the sum of angles**:
According to the property of triangles, we can write the equation:
\[ A + B + C = 180 \]
Substituting the expressions for A, B, and C, we get:
\[ 2x + 3x + 4x = 180 \]

4. **Combine like terms**:
Combine the terms on the left side:
\[ 9x = 180 \]

5. **Solve for \( x \)**:
Divide both sides by 9 to find \( x \):
\[ x = \frac{180}{9} = 20 \]

6. **Find the measure of angle B**:
Now that we have \( x \), we can find angle B:
\[ B = 3x = 3 \times 20 = 60 \text{ degrees} \]

### Conclusion:
The measure of angle B is **60 degrees**.