How The bisectors of any 2 consecutive angles of a parallelogram intersect at right angles?

I expect "consecutive angles" are any pair that aren't opposite.

Since they are co-interior angles between parallel lines, they are supplementarty (i.e. total 180 deg).

When you bisect them, the bisectors join to form a triangle. Two of its angles are halves of the "consecutive angles", and so they total half of 180 deg, which is 90 deg.

Hence the third angle is 90 deg (to give angle sum of the triangle as 180 deg), so the bisectors are perpendicular.