Which of the following shows that EFGH is a parallelogram for y=7 and z=9?

Option B: and , so is supplementary to both and , so EFGH is a parallelogram.

Option C: so EFGH is a parallelogram.

Option D: so EFGH is a parallelogram.

Explanation:

Option A: and so is supplementary to both and , so EFGH is a parallelogram

Let us substitute and in , and to determine the exact measures the angles of the parallelogram.

Substituting, we get, ,

Thus, because the measures of these angles are not equal.

Hence, Option A is not the correct answer.

Option B:   and , so is supplementary to both and , so EFGH is a parallelogram.

Let us substitute and in , and to determine the exact measures the angles of the parallelogram.

Thus, substituting, we have, ,

Hence, Option B is the correct answer.

Option C: so EFGH is a parallelogram.

To determine the angles, let us substitute in   and

Thus,

Since, the opposite angles of a parallelogram are equal, EFGH is a parallelogram.

Hence, Option C is the correct answer.

Option D: so EFGH is a parallelogram.

Let us substitute and in , and to determine the exact measures the angles of the parallelogram.

Substituting, we have, ,

Adding the angles E and G, we have,

By the property of parallelogram, any two adjacent angles add upto 180.

Thus, the adjacent angles E and G add upto 180.

Hence, Option D is the correct answer.