Question

1.1 find the values of x and y that ensure the quadrilateral is a parallelogram.2.) find the value of x and y that ensure the quadrilateral is a parallelogram.3.)4.)

Explanation:

1.1 Step1: Set equal opposite sides

$6x = 4x + 8$

1.1 Step2: Solve for x

$6x - 4x = 8 \implies 2x = 8 \implies x = 4$

1.1 Step3: Set equal opposite sides

$y + 2 = 2y$

1.1 Step4: Solve for y

$2y - y = 2 \implies y = 2$

2. Step1: Set equal opposite angles

$2x + 8 = 120$

2. Step2: Solve for x

$2x = 120 - 8 \implies 2x = 112 \implies x = 56$

2. Step3: Set adjacent angles supplementary

$5y + 120 = 180$

2. Step4: Solve for y

$5y = 180 - 120 \implies 5y = 60 \implies y = 12$

3. Step1: Set equal diagonal segments

$3x - 2 = 9$

3. Step2: Solve for x

$3x = 9 + 2 \implies 3x = 11 \implies x = \frac{11}{3}$

4. Step1: Set equal opposite sides

$3x - 31 = 4x - 1$

4. Step2: Solve for x

$4x - 3x = -31 + 1 \implies x = -30$

Answer:

1.1) $x=4$, $y=2$
2.) $x=56$, $y=12$
3.) $x=\frac{11}{3}$
4.) $x=-30$