The perimeter of a parallelogram is the sum of its sidelengths; its height is irrelevant. Also, opposite sides of a parallelogram are congruent.

The perimeter of parallelogram A is 

 inches;

The perimeter of parallelogram B is 

 inches.

(A) is greater.

All four sides of a rhombus have the same length, so we can find the perimeter of Rhombus  by taking the length of one side and multiplying it by four. Since , the perimeter is four times this, or .

Note that the length of  is actually irrelevant to the problem.

In Parallelogram , and  are adjoining sides; there is no specific rule for the relationship between their lengths. Therefore, no conclusion can be drawn of and , and no conclusion can be drawn of the relationship between and .

Opposite angles of a parallelogram must have the same measure, so the correct choice must have two pairs, each of the same angle measure. We can therefore eliminate  and  as choices. 

Also, the sum of the measures of the angles of any quadrilateral must be , so we add the angle measures of the remaining choices:

: 

, so we can eliminate this choice.

:

, so we can eliminate this choice.

; this is the correct choice.

The sum of two consecutive angles of a parallelogram is .

157 is the correct choice.

In Parallelogram , and are opposite angles and are therefore congruent. This means that

Both are positive, so .

The four sides of a rhombus, by defintion, have equal length, so

Since and are positive, .

It will be easier to look at these measurements as inches for the time being:

 and , so these are the lengths of the diagonals in inches.

The diagonals of a rhombus are each other's perpendicular bisector, so, as can be seen in the diagram below, one side of a rhombus and one half of each diagonal form a right triangle. If we let  be the length of one side of the rhombus, then this is the hypotenuse of that right triangle; its legs are one-half the lengths of the diagonals, or 15 and 36 inches.

By the Pythagorean Theorem, 

Each side of the rhombus measures 39 inches, and its perimeter is 

 inches.

Four yards is equal to  inches, so (A) is greater.

The diagonals of a rhombus are each other's perpendicular bisector, so, as can be seen in the diagram below, one side of a rhombus and one half of each diagonal form a right triangle. If the other diagonal has length , then the right triangle has hypotenuse 10 inches and legs one-half of one foot and  - that is, six inches and .

This triangle fits the well-known Pythagorean triple of 6-8-10, so

The other diagonal measures 16 inches. One and one-half feet is equal to 18 inches, making (B) greater.

The diagonals of a rhombus always intersect at right angles, so . The measures of the interior angles of the rhombus are irrelevant.