In quadrilateral pqrs, m∠rqs = 25° and ps = qr. what measure of ∠psq would confirm that pqrs is a parallelogram?

m∠psq = [ ]°

  25°

Step-by-step explanation:

If sides PS and QR are parallel, then ∠PSQ and ∠RQS are alternate interior angles, hence congruent. That is, ∠PSQ ≅ ∠RQS = 25°.

Comment on the problem statement

Confirming that two sides are parallel does not confirm the figure as a parallelogram. It could be a trapezoid. The given condition is necessary, but is not sufficient to do the confirmation.

add 5 subtract 1

step-by-step explanation:

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584