Question

6. Find the value of x for which ABCD must be a parallelogram.BO916x - 15CA30+ 11xD

Answer 1

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:

`|BC|=|AD|`

STEP 2: Write the measures of the two sides

`\begin{gathered} |BC|=16x-15 \\ |AD|=30+11x \end{gathered}`

STEP 3: Find the equation that applies

According to the statement in Step 1,

`16x-15=30+11x`

STEP 4: Solve for x

`\begin{gathered} 16x-15=30+11x \\ 16x-11x=30+15 \\ 5x=45 \\ (5x)/(5)=(45)/(5) \\ x=9 \end{gathered}`

Hence, x = 9