Question

select the correct answer from each drop - down menu. consider parallelogram abcd, where m∠abc = 135° and the length of diagonal ac is 41 units. note: figure not drawn to scale use the figure and given information to complete the statements. m∠bcd = 45 ° the length of segment cd is 7 units. the length of segment ae is 34, 67.5, 41, 20.5 units.

Explanation:

Step1: Find $\angle BCD$

In parallelogram $ABCD$, consecutive angles are supplementary.
$\angle ABC + \angle BCD = 180^\circ$
$\angle BCD = 180^\circ - 135^\circ = 45^\circ$

Step2: Find length of $CD$

In parallelogram $ABCD$, opposite sides are equal.
$AB = CD = 7$ units

Step3: Find length of $AE$

In parallelogram $ABCD$, diagonals bisect each other.
$AE = \frac{1}{2}AC = \frac{1}{2} \times 41 = 20.5$ units

Answer:

$m\angle BCD = 45$ °
The length of segment CD is 7 units.
The length of segment AE is 20.5 units.