In a parallelogram ABCD, the sum of any two consecutive angles is `180^(@)` and opposite angles are equal.
In a parallelogram `ABCD, angleD=115^(@)` , determine the measure of `angleA and angleB`

Options

A. `angleA = 85^@ , angleB = 115^@`
B. `angleA = 65^@ , angleB = 65^@`
C. `angleA = 65^@ , angleB = 115^@`
D. `angleA = 75^@ , angleB = 105^@`

Answer

To solve the problem, we will use the properties of a parallelogram. Let's go through the steps systematically.

### Step 1: Understand the properties of a parallelogram
In a parallelogram:
- Opposite angles are equal.
- The sum of any two consecutive angles is 180 degrees.

### Step 2: Identify the given information
We are given:
- Angle D = 115 degrees.

### Step 3: Find Angle B
Using the property that opposite angles are equal:
- Since angle B is opposite to angle D, we have:
\[ \text{Angle B} = \text{Angle D} = 115^\circ \]

### Step 4: Find Angle A
Using the property that the sum of two consecutive angles is 180 degrees:
- Angle A and Angle D are consecutive angles, so:
\[ \text{Angle A} + \text{Angle D} = 180^\circ \]
Substituting the value of angle D:
\[ \text{Angle A} + 115^\circ = 180^\circ \]

### Step 5: Solve for Angle A
To find angle A, we subtract 115 degrees from both sides:
\[ \text{Angle A} = 180^\circ - 115^\circ = 65^\circ \]

### Conclusion
Thus, the measures of the angles are:
- Angle A = 65 degrees
- Angle B = 115 degrees

### Summary of the Solution:
- Angle A = 65 degrees
- Angle B = 115 degrees