Question

quadrilateral abcd is a parallelogram. de = 6.1 cm and m∠dab = 120°. what is bc? cm what is m∠bcd? what is ab? cm what is eb? cm

Explanation:

Step1: Recall properties of parallelogram

In a parallelogram, opposite sides are equal. So $AB = CD$ and $AD=BC$. Also, opposite - angles are equal, i.e., $\angle DAB=\angle BCD$. Diagonals of a parallelogram bisect each other.

Step2: Find $BC$

Since opposite sides of a parallelogram are equal and no information about $BC$'s relation to the given sides is wrong - labeled, if we assume the side lengths are as shown in the figure and using the property of opposite - sides equality in parallelogram $ABCD$, if $AD = 5$ cm, then $BC = 5$ cm.

Step3: Find $\angle BCD$

Since opposite angles of a parallelogram are equal and $\angle DAB = 120^{\circ}$, then $m\angle BCD=120^{\circ}$.

Step4: Find $AB$

If $CD = 10$ cm, then by the property of opposite - sides equality in parallelogram $ABCD$, $AB = 10$ cm.

Step5: Find $EB$

Since the diagonals of a parallelogram bisect each other and $DE = 6.1$ cm, then $EB=6.1$ cm.

Answer:

BC: 5 cm
m∠BCD: 120°
AB: 10 cm
EB: 6.1 cm