Given the figure below is a special type of trapezoid and wx ii yz, which angle pairs can be proven supplementary by the given information? select all that apply

we know that

supplementary angle are those angles whose sum is 180

we are given that

WX is parallel to ZY

and

WZ is parallel to XY

so, WXYZ is a parallelogram

and we know that

opposite angles are always equal

W=Y

Z=X

and sum of all angle in any quadrilateral is 360

so, we get

and we will also get

so,

option-A , C , E.......Answer

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.