If the difference between two supplementary angles is 40 then the angles are -

Options

A. `40^@, 140^@`
B. `80^@,100^@`
C. `110^@,70^@`
D. `65^@,115^@`

Answer

To solve the problem of finding two supplementary angles where the difference between them is 40 degrees, we can follow these steps:

### Step 1: Define the Angles
Let the two angles be \( x \) and \( y \). According to the problem, we know that:
- The sum of the angles is 180 degrees (since they are supplementary).
- The difference between the angles is 40 degrees.

### Step 2: Set Up the Equations
From the information given, we can set up the following equations:
1. \( x + y = 180 \) (Equation 1)
2. \( x - y = 40 \) (Equation 2)

### Step 3: Solve for One Variable
We can solve Equation 2 for \( x \):
\[ x = y + 40 \]

### Step 4: Substitute into the First Equation
Now substitute \( x \) from Equation 2 into Equation 1:
\[ (y + 40) + y = 180 \]

### Step 5: Simplify the Equation
Combine like terms:
\[ 2y + 40 = 180 \]

### Step 6: Isolate the Variable
Subtract 40 from both sides:
\[ 2y = 180 - 40 \]
\[ 2y = 140 \]

### Step 7: Solve for \( y \)
Divide both sides by 2:
\[ y = \frac{140}{2} = 70 \]

### Step 8: Find \( x \)
Now substitute the value of \( y \) back into the equation for \( x \):
\[ x = y + 40 = 70 + 40 = 110 \]

### Step 9: State the Angles
The two supplementary angles are:
\[ x = 110^\circ \quad \text{and} \quad y = 70^\circ \]

### Final Answer
The angles are \( 110^\circ \) and \( 70^\circ \).

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