Two supplementary angles differ by `44^(@)` . Find the angles.

Options

A. `212^(@),68^(@)`
B. `112^(@),88^(@)`
C. `112^(@),68^(@)`
D. `116^(@),68^(@)`

Answer

To solve the problem of finding two supplementary angles that differ by 44 degrees, we can follow these steps:

### Step 1: Define the Angles
Let the first angle be \( X \) degrees and the second angle be \( Y \) degrees.

### Step 2: Set Up the Equations
Since the angles are supplementary, we know that:
\[ X + Y = 180 \quad \text{(1)} \]
We are also given that the difference between the two angles is 44 degrees:
\[ X - Y = 44 \quad \text{(2)} \]

### Step 3: Solve the Equations
We can solve these two equations simultaneously.

From equation (1), we can express \( Y \) in terms of \( X \):
\[ Y = 180 - X \quad \text{(3)} \]

Now, substitute equation (3) into equation (2):
\[ X - (180 - X) = 44 \]
This simplifies to:
\[ X - 180 + X = 44 \]
\[ 2X - 180 = 44 \]

### Step 4: Isolate \( X \)
Now, add 180 to both sides:
\[ 2X = 44 + 180 \]
\[ 2X = 224 \]
Now, divide both sides by 2:
\[ X = \frac{224}{2} \]
\[ X = 112 \]

### Step 5: Find \( Y \)
Now that we have \( X \), we can find \( Y \) using equation (3):
\[ Y = 180 - X \]
\[ Y = 180 - 112 \]
\[ Y = 68 \]

### Conclusion
The two supplementary angles are:
- First angle \( X = 112^\circ \)
- Second angle \( Y = 68^\circ \)

### Final Answer
The angles are \( 112^\circ \) and \( 68^\circ \).

---