Two angles are supplementary and are in the ratio `2 : 4`. What is the value of one of the larger angle ?

Options

A. `240^(@)`
B. `108^(@)`
C. `80^(@)`
D. `120^(@)`

Answer

To solve the problem of finding the value of one of the larger angles that are supplementary and in the ratio of 2:4, follow these steps:

### Step 1: Understand the Concept of Supplementary Angles
Supplementary angles are two angles whose sum is 180 degrees.

### Step 2: Set Up the Ratio
Given that the angles are in the ratio of 2:4, we can express the angles in terms of a variable. Let the first angle be \(2x\) and the second angle be \(4x\).

### Step 3: Write the Equation for Supplementary Angles
Since the angles are supplementary, we can write the equation:
\[ 2x + 4x = 180 \]

### Step 4: Combine Like Terms
Combine the terms on the left side of the equation:
\[ 6x = 180 \]

### Step 5: Solve for \(x\)
To find \(x\), divide both sides of the equation by 6:
\[ x = \frac{180}{6} = 30 \]

### Step 6: Find the Larger Angle
Now that we have the value of \(x\), we can find the larger angle, which is \(4x\):
\[ 4x = 4 \times 30 = 120 \]

### Final Answer
The value of the larger angle is \(120\) degrees.

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