If the angles, in degrees, of a triangle are x, `3 x + 20` and 6x, the triangle must be

Options

A. isosceles
B. obtuse
C. acute
D. right

Answer

To solve the problem, we need to find the angles of the triangle given as \( x \), \( 3x + 20 \), and \( 6x \). We will use the property that the sum of the angles in a triangle is equal to \( 180^\circ \).

### Step-by-Step Solution:

1. **Write the equation for the sum of the angles**:
\[ x + (3x + 20) + 6x = 180 \]

2. **Combine like terms**:
\[ x + 3x + 20 + 6x = 180 \]
\[ 10x + 20 = 180 \]

3. **Isolate the variable \( x \)**:
Subtract \( 20 \) from both sides:
\[ 10x = 180 - 20 \]
\[ 10x = 160 \]

4. **Solve for \( x \)**:
Divide both sides by \( 10 \):
\[ x = \frac{160}{10} = 16 \]

5. **Calculate the angles**:
- First angle:
\[ x = 16^\circ \]
- Second angle:
\[ 3x + 20 = 3(16) + 20 = 48 + 20 = 68^\circ \]
- Third angle:
\[ 6x = 6(16) = 96^\circ \]

6. **Check the angles**:
Now, we verify if the angles add up to \( 180^\circ \):
\[ 16 + 68 + 96 = 180^\circ \]
This confirms that our calculations are correct.

7. **Determine the type of triangle**:
The angles are \( 16^\circ \), \( 68^\circ \), and \( 96^\circ \). Since one of the angles (96°) is greater than \( 90^\circ \), the triangle is classified as an obtuse triangle.

### Final Answer:
The triangle must be an obtuse triangle.