The bisectors of any two adjacent angles of a parallelogram intersect at an angle equal to __________.

The bisectors of any two adjacent angles of a parallelogram intersect at an angle equal to half the sum of the two angles.

Here's the step by step explanation:

1. Let's consider a parallelogram ABCD. Let ∠DAB = a and ∠ABC = b.

2. The bisectors of these two angles will divide them into two equal parts. So, the bisector of ∠DAB will create two angles of a/2 and the bisector of ∠ABC will create two angles of b/2.

3. These bisectors will intersect at a point, say O.

4. Now, ∠AOB will be equal to a/2 + b/2 = (a+b)/2.

5. But, in a parallelogram, the sum of two adjacent angles is 180°. So, a + b = 180°.

6. Therefore, ∠AOB = (a+b)/2 = 180°/2 = 90°.

So, the bisectors of any two adjacent angles of a parallelogram intersect at an angle equal to 90°.