In a parallelogram ABCD, angleA = 115 degree. The measure of angle D is equal to

Options

A. `115^(@)`
B. `65^(@)`
C. `135^(@)`
D. `165^(@)`

Answer

To find the measure of angle D in parallelogram ABCD where angle A is given as 115 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of a Parallelogram**:
In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (i.e., they add up to 180 degrees).

2. **Identify the Given Information**:
We know that angle A = 115 degrees.

3. **Set Up the Equation for Adjacent Angles**:
Since angle A and angle D are adjacent angles in the parallelogram, we can write the equation:
\[ \text{angle A} + \text{angle D} = 180^\circ \]

4. **Substitute the Known Value**:
Substitute the value of angle A into the equation:
\[ 115^\circ + \text{angle D} = 180^\circ \]

5. **Solve for Angle D**:
To find angle D, subtract 115 degrees from both sides of the equation:
\[ \text{angle D} = 180^\circ - 115^\circ \]
\[ \text{angle D} = 65^\circ \]

6. **Conclusion**:
Therefore, the measure of angle D is 65 degrees.

### Final Answer:
Angle D = 65 degrees.

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