Question

finding measures find the measure in parallelogram abcd. explain your reasoning.

1. de
2. ba
3. bc
4. $m\angle cda$
5. $m\angle abc$
6. $m\angle bcd$

Explanation:

Step1: Recall parallelogram properties

In a parallelogram: opposite sides are equal, diagonals bisect each other, consecutive angles are supplementary, opposite angles are equal.

Step2: Solve for DE

Diagonals bisect each other, so $DE = BE$.
$DE = 10$

Step3: Solve for BA

Opposite sides are equal, so $BA = CD$.
$BA = 11$

Step4: Solve for BC

Opposite sides are equal, so $BC = AD$.
$BC = 12$

Step5: Solve for $m\angle CDA$

Opposite angles are equal, so $m\angle CDA = m\angle ABC$. $m\angle ABC = 120^\circ$, so $m\angle CDA = 120^\circ$

Step6: Solve for $m\angle ABC$

Given directly in the diagram.
$m\angle ABC = 120^\circ$

Step7: Solve for $m\angle BCD$

Consecutive angles are supplementary, so $m\angle BCD + m\angle ABC = 180^\circ$.
$m\angle BCD = 180^\circ - 120^\circ = 60^\circ$

Answer:

1. $DE = 10$
2. $BA = 11$
3. $BC = 12$
4. $m\angle CDA = 120^\circ$
5. $m\angle ABC = 120^\circ$
6. $m\angle BCD = 60^\circ$