In a parallelogram ABCD, bisectors of consecutive angles A and B intersect at P. Find the measure of `angle APB` :

Options

A. `90^(@)`
B. `60^(@)`
C. `120^(@)`
D. data insufficient

Answer

To solve the problem, we need to find the measure of angle APB in the parallelogram ABCD, where P is the intersection of the angle bisectors of angles A and B.

### Step-by-Step Solution:

1. **Understanding the Properties of a Parallelogram**:
In a parallelogram, adjacent angles are supplementary. Therefore, we have:
\[ \angle A + \angle B = 180^\circ \]

2. **Using the Angle Bisector**:
Let’s denote:
- \(\angle A = a\)
- \(\angle B = b\)

From the property of the parallelogram, we know:
\[ a + b = 180^\circ \]

The angle bisector of angle A divides it into two equal parts:
\[ \angle APD = \frac{a}{2} \]

Similarly, the angle bisector of angle B divides it into two equal parts:
\[ \angle BPC = \frac{b}{2} \]

3. **Finding the Measure of Angle APB**:
In triangle APB, the sum of the angles is:
\[ \angle APB + \angle APD + \angle BPC = 180^\circ \]

Substituting the values we have:
\[ \angle APB + \frac{a}{2} + \frac{b}{2} = 180^\circ \]

Since \(a + b = 180^\circ\), we can replace \(\frac{a}{2} + \frac{b}{2}\) with:
\[ \frac{a + b}{2} = \frac{180^\circ}{2} = 90^\circ \]

Therefore, we can rewrite the equation as:
\[ \angle APB + 90^\circ = 180^\circ \]

4. **Solving for Angle APB**:
Rearranging gives us:
\[ \angle APB = 180^\circ - 90^\circ = 90^\circ \]

### Conclusion:
The measure of angle APB is \(90^\circ\).