Angles which are both supplementary and vertically opposite are

Options

A. `95^(@) , 85^(@)`
B. `90^(@) , 90^(@)`
C. `100^(@) , 80^(@)`
D. `45^(@) , 45^(@)`

Answer

To solve the question, "Angles which are both supplementary and vertically opposite are," we will follow these steps:

### Step 1: Understand the Definitions
- **Supplementary Angles**: Two angles are supplementary if the sum of their measures is equal to 180 degrees.
- **Vertically Opposite Angles**: When two lines intersect, they form two pairs of opposite angles. These angles are called vertically opposite angles, and they are equal in measure.

### Step 2: Set Up the Angles
Let’s denote the two angles as angle X and angle Y. According to the definitions:
- If angle X and angle Y are supplementary, then:
\[ X + Y = 180^\circ \]

### Step 3: Establish the Relationship of Vertically Opposite Angles
Since angle X and angle Y are also vertically opposite angles, we have:
- Vertically opposite angles are equal, so:
\[ X = Y \]

### Step 4: Substitute and Solve
Now, substituting \( Y \) with \( X \) in the supplementary angle equation:
\[ X + X = 180^\circ \]
This simplifies to:
\[ 2X = 180^\circ \]
Dividing both sides by 2 gives:
\[ X = 90^\circ \]

### Step 5: Conclusion
Since \( Y \) is equal to \( X \), we also have:
\[ Y = 90^\circ \]
Thus, both angles are 90 degrees. Therefore, the angles which are both supplementary and vertically opposite are:
\[ 90^\circ \text{ and } 90^\circ \]