The angles of a triangle are in the ratio `3 : 5 : 7`. The triangle is

Options

A. acute angled
B. obtuse angled
C. right angled
D. an isosceles triangle

Answer

To solve the problem of finding the type of triangle based on the ratio of its angles, follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio of Angles**: The angles of the triangle are given in the ratio of 3:5:7. Let's denote the angles as \( A \), \( B \), and \( C \). Therefore, we can express them as:
\[ A = 3x, \quad B = 5x, \quad C = 7x \]

2. **Use the Triangle Angle Sum Property**: The sum of the angles in any triangle is always 180 degrees. Therefore, we can write the equation:
\[ A + B + C = 180^\circ \]
Substituting the expressions for \( A \), \( B \), and \( C \):
\[ 3x + 5x + 7x = 180^\circ \]

3. **Combine Like Terms**: Combine the terms on the left side:
\[ (3 + 5 + 7)x = 180^\circ \]
This simplifies to:
\[ 15x = 180^\circ \]

4. **Solve for \( x \)**: Divide both sides by 15 to find \( x \):
\[ x = \frac{180^\circ}{15} = 12^\circ \]

5. **Calculate Each Angle**:
- For angle \( A \):
\[ A = 3x = 3 \times 12^\circ = 36^\circ \]
- For angle \( B \):
\[ B = 5x = 5 \times 12^\circ = 60^\circ \]
- For angle \( C \):
\[ C = 7x = 7 \times 12^\circ = 84^\circ \]

6. **Determine the Type of Triangle**: Now we have the angles:
\[ A = 36^\circ, \quad B = 60^\circ, \quad C = 84^\circ \]
Since all angles are less than 90 degrees, this triangle is classified as an **acute triangle**.

### Final Answer:
The triangle is an **acute triangle**.