Question

partially correct
your answer is incorrect.
· $m\angle ebc$: your answer is incorrect.
in the rectangle below, $ae = 4x+5$, $ce = 6x-9$, and $m\angle aed=112^\circ$.
find $bd$ and $m\angle ebc$.
your answer
$bd = 66$
$m\angle ebc = 56^\circ$
hw 7.5 (with 7.4)
due today 11:59 pm

Explanation:

Step1: Solve for $x$ (diagonals bisect)

Since diagonals of a rectangle bisect each other, $AE=CE$.
$$4x+5=6x-9$$
$$14=2x$$
$$x=7$$

Step2: Calculate length of $AE$

Substitute $x=7$ into $AE=4x+5$.
$$AE=4(7)+5=28+5=33$$

Step3: Find length of $BD$

Diagonals of a rectangle are equal, so $BD=AC=2AE$.
$$BD=2\times33=66$$

Step4: Find $\angle AEB$

$\angle AED$ and $\angle AEB$ are supplementary.
$$m\angle AEB=180^\circ-112^\circ=68^\circ$$

Step5: Find $\angle EBC$

$\triangle AEB$ is isosceles, so $\angle EBA=\frac{180^\circ-68^\circ}{2}=56^\circ$.
$\angle ABC=90^\circ$, so $m\angle EBC=90^\circ-56^\circ$.
$$m\angle EBC=34^\circ$$

Answer:

$BD = 66$
$m\angle EBC = 34^\circ$