Answer :

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: State the appropriate side theorem that applies to the given question

Opposite sides of a parallelogram have equal lengths. This means that:

[tex]|BC|=|AD|[/tex]

STEP 2: Write the measures of the two sides

[tex]\begin{gathered} |BC|=16x-15 \\ |AD|=30+11x \end{gathered}[/tex]

STEP 3: Find the equation that applies

According to the statement in Step 1,

[tex]16x-15=30+11x[/tex]

STEP 4: Solve for x

[tex]\begin{gathered} 16x-15=30+11x \\ 16x-11x=30+15 \\ 5x=45 \\ \frac{5x}{5}=\frac{45}{5} \\ x=9 \end{gathered}[/tex]

Hence, x = 9

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