`angleABC` and `angleABD` form a linear pair. If `angleABC=30^(@)`, then `angleABD=`...........

Options

A. `30^(@)`
B. `60^(@)`
C. `150^(@)`
D. `15^(@)`

Answer

To solve the problem, we will use the property of linear pairs of angles. A linear pair of angles are two adjacent angles whose non-common sides form a straight line. This means that the sum of the angles in a linear pair is always equal to 180 degrees.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- We know that angle ABC and angle ABD form a linear pair.
- We are given that angle ABC = 30 degrees.

2. **Use the Linear Pair Property**:
- Since angle ABC and angle ABD form a linear pair, we can write the equation:
\[ \text{angle ABC} + \text{angle ABD} = 180^\circ \]

3. **Substitute the Known Value**:
- Substitute the value of angle ABC into the equation:
\[ 30^\circ + \text{angle ABD} = 180^\circ \]

4. **Solve for angle ABD**:
- To find angle ABD, subtract 30 degrees from both sides of the equation:
\[ \text{angle ABD} = 180^\circ - 30^\circ \]
- Calculate the right side:
\[ \text{angle ABD} = 150^\circ \]

5. **Conclusion**:
- Therefore, the measure of angle ABD is 150 degrees.

### Final Answer:
\[ \text{angle ABD} = 150^\circ \]