Question

what value of x and y will make the polygon a parallelogram?
7)
8)
9)
10)

Explanation:

7)

Step1: Use the property of parallelogram (opposite sides are equal)

For the sides: \(3x = 6\)

Step2: Solve for \(x\)

\(x=\frac{6}{3}=2\)

Step3: Use the other pair of opposite sides

\(x + 2=y-1\), substitute \(x = 2\)
\(2+2=y - 1\)

Step4: Solve for \(y\)

\(y=2 + 2+1=5\)

Step1: Use the property of parallelogram (consecutive angles are supplementary)

\(105+15x = 180\)

Step2: Solve for \(x\)

\(15x=180 - 105=75\), \(x=\frac{75}{15}=5\)

Step3: Use the property of parallelogram (opposite angles are equal)

\(y = 15x\), substitute \(x = 5\)

Step1: Use the property of parallelogram (diagonals bisect each other)

\(3x=12\)

Step2: Solve for \(x\)

\(x = 4\)

Step3: Also \(x + y=5y\), substitute \(x = 4\)

\(4+y=5y\)

Step4: Solve for \(y\)

\(4y=4\), \(y = 1\)

Answer:

\(x = 2,y = 5\)

8)