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Answer 1

Answer:

I will assume that ABCD is a parallelogram.

1. In a parallelogram, opposite sides are congruent so 3x = 18 which means x = 6.

2. The diagonals of a parallelogram bisect each other so BE is half of BD, therefore, BD = 7.5.

3. Consecutive angles of a parallelogram are supplementary so m∠ADC = 180° - 135° = 45°.

4. Consecutive angles of parallelograms are supplementary so 2x + 10 + 135 = 180 → 2x + 145 = 180 → 2x = 35 → x = 17.5°.

5.  Again, the diagonals bisect each other so -6 + 8v = 9v - 10 → v = 4.

6. DA || BC so ∠DAC and ∠ACB are (congruent) alternate interior angles, therefore, m∠DAC = 37°.

7. The area of a parallelogram is base * height; we know base = 18 and height = 21 u so area = 378 u.