If two supplementary angles are in the ratio `13:5` find the greater angle :

Options

A. `130^(@)`
B. `65^(@)`
C. `230^(@)`
D. `28^(@)`

Answer

To solve the problem of finding the greater angle when two supplementary angles are in the ratio of 13:5, follow these steps:

### Step-by-Step Solution:

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

2. **Set Up the Angles Using the Ratio**:
Let the two angles be represented as:
- First angle = \( 13x \)
- Second angle = \( 5x \)

3. **Write the Equation for Supplementary Angles**:
Since the angles are supplementary, we can write the equation:
\[ 13x + 5x = 180 \]

4. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ 18x = 180 \]

5. **Solve for \( x \)**:
Divide both sides of the equation by 18 to find \( x \):
\[ x = \frac{180}{18} = 10 \]

6. **Calculate the Angles**:
Now substitute \( x \) back into the expressions for the angles:
- First angle:
\[ 13x = 13 \times 10 = 130 \text{ degrees} \]
- Second angle:
\[ 5x = 5 \times 10 = 50 \text{ degrees} \]

7. **Identify the Greater Angle**:
Compare the two angles:
- First angle = 130 degrees
- Second angle = 50 degrees

Therefore, the greater angle is:
\[ \text{Greater angle} = 130 \text{ degrees} \]

### Final Answer:
The greater angle is **130 degrees**.

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