If two supplementary angles are in the ratio `1 : 2`, then the bigger angle is

Options

A. `120^(@)`
B. `125^(@)`
C. `110^(@)`
D. `90^(@)`

Answer

To solve the problem of finding the bigger angle when two supplementary angles are in the ratio of 1:2, follow these steps:

### Step 1: Understand the concept of supplementary angles
Supplementary angles are two angles whose sum is equal to 180 degrees.

### Step 2: Set up the ratio
Let the two angles be represented as:
- First angle = \( x \)
- Second angle = \( 2x \) (since the ratio is 1:2)

### Step 3: Write the equation for supplementary angles
According to the definition of supplementary angles, we can write the equation:
\[ x + 2x = 180 \]

### Step 4: Simplify the equation
Combine like terms:
\[ 3x = 180 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 3:
\[ x = \frac{180}{3} \]
\[ x = 60 \]

### Step 6: Find the second angle
Now, substitute \( x \) back into the expression for the second angle:
\[ 2x = 2 \times 60 = 120 \]

### Step 7: Identify the bigger angle
The two angles are:
- First angle = \( 60 \) degrees
- Second angle = \( 120 \) degrees

Thus, the bigger angle is:
\[ \text{Bigger angle} = 120 \text{ degrees} \]

### Final Answer
The bigger angle is **120 degrees**.

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