Question

use the parallelogram below to answer the following questions.
what is the value of ( x )?
( x = )
what is the length of ( overline{ab} )?
( ab = ) in

Explanation:

Step1: Recall parallelogram side property

In a parallelogram, opposite sides are equal. So \( AB = CD \), which means \( 8x + 13 = 6x + 21 \).

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides: \( 8x - 6x + 13 = 6x - 6x + 21 \), simplifying to \( 2x + 13 = 21 \).
Subtract 13 from both sides: \( 2x + 13 - 13 = 21 - 13 \), giving \( 2x = 8 \).
Divide by 2: \( \frac{2x}{2} = \frac{8}{2} \), so \( x = 4 \).

Step3: Find length of \( \overline{AB} \)

Substitute \( x = 4 \) into \( 8x + 13 \): \( 8(4) + 13 = 32 + 13 = 45 \).

Answer:

For \( x \): \( \boldsymbol{4} \)
For length of \( \overline{AB} \): \( \boldsymbol{45} \) in