Answer:
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:
