The angles of a triangle are in the ratio 1:3:5. Find the measure of each of the angles.

Answer

To find the measures of the angles of a triangle given in the ratio 1:3:5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The angles of the triangle are given in the ratio 1:3:5. This means we can express the angles in terms of a variable \( x \). Let:
- Angle A = \( 1x \)
- Angle B = \( 3x \)
- Angle C = \( 5x \)

2. **Use the Triangle Angle Sum Property**: The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
Substituting the expressions for the angles:
\[ 1x + 3x + 5x = 180^\circ \]

3. **Combine Like Terms**: Combine the terms on the left side of the equation:
\[ (1x + 3x + 5x) = 9x \]
So, we have:
\[ 9x = 180^\circ \]

4. **Solve for \( x \)**: To find the value of \( x \), divide both sides of the equation by 9:
\[ x = \frac{180^\circ}{9} = 20^\circ \]

5. **Calculate Each Angle**:
- Angle A = \( 1x = 1 \times 20^\circ = 20^\circ \)
- Angle B = \( 3x = 3 \times 20^\circ = 60^\circ \)
- Angle C = \( 5x = 5 \times 20^\circ = 100^\circ \)

6. **Conclusion**: The measures of the angles of the triangle are:
- Angle A = \( 20^\circ \)
- Angle B = \( 60^\circ \)
- Angle C = \( 100^\circ \)

### Summary of Angles:
- Angle A = \( 20^\circ \)
- Angle B = \( 60^\circ \)
- Angle C = \( 100^\circ \)