Two supplementary angles are in the ratio of `2: 7`, find the angles

Answer

To solve the problem of finding two supplementary angles that are in the ratio of 2:7, follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Supplementary Angles**:
Supplementary angles are two angles whose sum is equal to 180 degrees.

2. **Set Up the Ratio**:
Given the ratio of the two angles is 2:7, we can represent the angles in terms of a variable \( x \). Let:
- First angle = \( 2x \)
- Second angle = \( 7x \)

3. **Write the Equation for Supplementary Angles**:
Since the angles are supplementary, we can write the equation:
\[ 2x + 7x = 180 \]

4. **Combine Like Terms**:
Combine the terms on the left side:
\[ 9x = 180 \]

5. **Solve for \( x \)**:
Divide both sides by 9 to find \( x \):
\[ x = \frac{180}{9} = 20 \]

6. **Calculate Each Angle**:
Now that we have \( x \), we can find each angle:
- First angle = \( 2x = 2 \times 20 = 40 \) degrees
- Second angle = \( 7x = 7 \times 20 = 140 \) degrees

7. **Final Answer**:
The two supplementary angles are:
- First angle: 40 degrees
- Second angle: 140 degrees