ABCD is a parallelogram. Find the value of x, y, w, and z.

Summary:

Step-by-step explanation:

Given

We know opposite sides of a parallelogram are equal.

Therefore,

now subtitute AD = x-28 and BC = 3x in AD = BC

AD = BC

x-28 = 3x

switch sides

3x = x-28

subracting x from both sides

3x-x = x-28+x

2x = -28

divide both sides by 2

2x/2 = -28/2

x = -14

Therefore,

The value of x = -14

Now subtitute AB = 12 and CD = 2/3y in AB = CD

AB = CD

12 = 2/3y

switching sides

2/3y = 12

y = 3/2 × 12

y = 18

Therefore,

The value of y = 18

We also know that the opposite angles of a parallelogram are equal.

Therefore,

5w = 70°

divide both sides by 5

5w/5 = 70°/5

w = 14

Therefore,

The value of w = 14

We know that the sum of the measures of the adjacent angles of a parallelogram is 180°.

Here,

m∠B = 70°.

m∠A = (3w+2z)°

As m∠B is adjacent to m∠A.

so

m∠A + m∠B = 180°

so substituting m∠B = 70° and m∠A = (3w+2z)° in the equation

70° + (3w+2z)° =  180°

now substituting w = 14 in the equation

70° +  (3(14) + 2z)° = 180°

70° + (42+2z)° =  180°

70° + 42 + 2z = 180°

112 + 2z = 180°

2z = 180° - 112

2z = 68

divide both sides by 2

2z/z = 68/2

z = 34

Therefore,

The value of z = 14

Summary:

ou would have 12 of each

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.