If `z^(@) and (z + 50)^(@)` are supplements of each other, find the value of z

Answer

To solve the problem, we need to find the value of \( z \) given that \( z \) and \( (z + 50) \) are supplementary angles. Supplementary angles are two angles whose sum is \( 180^\circ \).

### Step-by-Step Solution:

1. **Understand the definition of supplementary angles**:
- If two angles are supplementary, their sum is equal to \( 180^\circ \).
- In this case, the angles are \( z \) and \( z + 50 \).

2. **Set up the equation**:
- We can write the equation based on the definition of supplementary angles:
\[ z + (z + 50) = 180 \]

3. **Simplify the equation**:
- Combine like terms:
\[ z + z + 50 = 180 \]
\[ 2z + 50 = 180 \]

4. **Isolate the term with \( z \)**:
- Subtract \( 50 \) from both sides:
\[ 2z = 180 - 50 \]
\[ 2z = 130 \]

5. **Solve for \( z \)**:
- Divide both sides by \( 2 \):
\[ z = \frac{130}{2} \]
\[ z = 65 \]

6. **Conclusion**:
- The value of \( z \) is \( 65^\circ \).

### Final Answer:
The value of \( z \) is \( 65^\circ \).