what is the length of segment eb in parallelogram abcd? 30 units 34.5 units 69 units 138 units

Explanation:

Step1: Apply parallelogram diagonal property

In a parallelogram, the diagonals bisect each other. So, $AE = EC$ and $DE=EB$. Here, $AE = 2x + 9$ and $EC=3x - 21$. Set up the equation $2x+9 = 3x - 21$. $2x+9=3x - 21$

Step2: Solve for x

Subtract $2x$ from both sides: $9=x - 21$. Then add 21 to both sides. $x=9 + 21=30$

Step3: Find length of EB

Since $EB=3x - 21$, substitute $x = 30$ into the expression. $EB=3\times30-21=90 - 21=69$

Answer:

69 units