The ratio of supplementary angle is 2:3 then find the angle:

Options

A. `30^@,45^@`
B. `36^@,54^@`
C. `72^@,108^@`
D. `66^@,114^@`

Answer

To solve the problem of finding the angles whose ratio is 2:3 and are supplementary, we can 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
Given the ratio of the angles is 2:3, we can represent the angles as:
- First angle = 2x
- Second angle = 3x

### Step 3: Write the equation for supplementary angles
Since the sum of the angles is 180 degrees, we can write the equation:
\[ 2x + 3x = 180 \]

### Step 4: Combine like terms
Combine the terms on the left side of the equation:
\[ 5x = 180 \]

### Step 5: Solve for x
To find the value of x, divide both sides of the equation by 5:
\[ x = \frac{180}{5} = 36 \]

### Step 6: Calculate the angles
Now, substitute the value of x back into the expressions for the angles:
- First angle = \( 2x = 2 \times 36 = 72 \) degrees
- Second angle = \( 3x = 3 \times 36 = 108 \) degrees

### Step 7: State the final answer
The two supplementary angles are 72 degrees and 108 degrees.