Question

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

Answer 1

Summary:

• The value of x = -14

• The value of y = 18

• The value of w = 14

• The value of z = 14

Explanation:

Given

• The parallelogram ABCD

• AD = x-28

• BC = 3x

• AB = 12

• CD = 2/3y

We know opposite sides of a parallelogram are equal.

Therefore,

• AD = BC

• AB = CD

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:

• The value of x = -14

• The value of y = 18

• The value of w = 14

• The value of z = 14