Question

1. find the value of x for which abcd must be a parallelogram.

b 16x - 15 c
a 30 + 11x d
41
9
3
1

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - sides are equal. So, if \(ABCD\) is a parallelogram, then \(BC = AD\).
We have \(BC=16x - 15\) and \(AD = 30+11x\).
Set up the equation \(16x−15 = 30 + 11x\).

Step2: Solve the equation for \(x\)

Subtract \(11x\) from both sides of the equation:
\(16x-11x−15=30 + 11x-11x\)
\(5x-15 = 30\).
Then add 15 to both sides:
\(5x-15 + 15=30 + 15\)
\(5x=45\).
Divide both sides by 5:
\(x=\frac{45}{5}=9\).

Answer:

9