The angles of a triangle are in the ration `1:2:3`. Find the measure of each angle of the triangle.

Answer

To find the measure of each angle of a triangle when the angles are in the ratio of 1:2:3, we can follow these steps:

### Step-by-Step Solution:

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

2. **Set Up the Equation**:
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ 1x + 2x + 3x = 180 \]

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

4. **Solve for x**:
To find the value of x, divide both sides of the equation by 6:
\[ x = \frac{180}{6} = 30 \]

5. **Calculate Each Angle**:
Now that we have the value of x, we can find each angle:
- First angle = 1x = 1 * 30 = 30 degrees
- Second angle = 2x = 2 * 30 = 60 degrees
- Third angle = 3x = 3 * 30 = 90 degrees

6. **State the Final Answer**:
The measures of the angles of the triangle are:
- First angle: 30 degrees
- Second angle: 60 degrees
- Third angle: 90 degrees

### Final Answer:
The angles of the triangle are 30 degrees, 60 degrees, and 90 degrees.

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