Each diagonal of a quadrilateral bisects a pair of opposite angles of the quadrilateral. what is the most precise name for the quadrilateral? a. parallelogram b. rhombus c. rectangle d. square

I like the word "precise name", because two answers fit the bill.

One (square) will fit the bill but less general.
The other (rhombus) will fit the bill and INCLUDE all cases of squares, since a square is a rhombus!

Reasoning:
A rhombus or a square both have all four sides equal.
Diagonals intersect each other at 90 degrees.  
As well, diagonals divide figure into two congruent isosceles triangles, hence bisects the angles at the vertices.

40 & 50 in the right corner are the complementary angles as when placed in a sum (added together) they make 90°