Angles of the triangle are in the ratio of 1:2:3. Choose the correct triangle for the given ratio.

Options

A. Equilateral
B. Isosceles
C. Right angle
D. Obtuse angled

Answer

To solve the problem of finding the angles of a triangle given in the ratio of 1:2:3, 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 follows:
- First angle = \( x \)
- Second angle = \( 2x \)
- Third angle = \( 3x \)

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

3. **Combine Like Terms:**
Combine the terms on the left side of the equation:
\[ 6x = 180^\circ \]

4. **Solve for \( x \):**
Divide both sides of the equation by 6 to find the value of \( x \):
\[ x = \frac{180^\circ}{6} = 30^\circ \]

5. **Calculate Each Angle:**
Now that we have \( x \), we can find the measures of each angle:
- First angle = \( x = 30^\circ \)
- Second angle = \( 2x = 2 \times 30^\circ = 60^\circ \)
- Third angle = \( 3x = 3 \times 30^\circ = 90^\circ \)

6. **Identify the Type of Triangle:**
Since one of the angles is \( 90^\circ \), we can conclude that the triangle is a right-angled triangle.

### Final Answer:
The angles of the triangle are \( 30^\circ, 60^\circ, \) and \( 90^\circ \), making it a right-angled triangle.

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