If the angles of a triangle are in the ratio `5 : 3 : 2`, then the triangle could be

Options

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

Answer

To solve the problem of finding the angles of a triangle that are in the ratio of 5:3:2, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The angles of the triangle are given in the ratio of 5:3:2. This means we can express the angles as:
- First angle = 5x
- Second angle = 3x
- Third angle = 2x

2. **Use the Triangle Angle Sum Property**: We know that the sum of the angles in a triangle is always 180 degrees. Therefore, we can set up the equation:
\[ 5x + 3x + 2x = 180 \]

3. **Combine Like Terms**: Combine the terms on the left side of the equation:
\[ 10x = 180 \]

4. **Solve for x**: To find the value of x, divide both sides of the equation by 10:
\[ x = \frac{180}{10} = 18 \]

5. **Calculate Each Angle**:
- First angle:
\[ 5x = 5 \times 18 = 90 \text{ degrees} \]
- Second angle:
\[ 3x = 3 \times 18 = 54 \text{ degrees} \]
- Third angle:
\[ 2x = 2 \times 18 = 36 \text{ degrees} \]

6. **Identify the Type of Triangle**: The angles we calculated are 90 degrees, 54 degrees, and 36 degrees. Since one of the angles is 90 degrees, this triangle is a right-angled triangle.

### Conclusion:
The triangle with angles in the ratio of 5:3:2 is a right-angled triangle.

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