Answer:
∠ZVW= 45
∠ZWV = 31
x=1
Step-by-step explanation:
Properties of a Parallelogram ( including diagonals )
Diagonals of a parallelogram bisect each other.
The diagonals are cut into two equal parts
Opposite angles are congruent
Given this information we need to find x, ∠ZVW and ∠ ZWV
First lets find x
Like stated previously diagonals cut each other into two equal parts
That being said segment WZ ≅ segment ZY
Knowing this we create an equation
2z-1=1
step 1 add 1 to each side
-1 + 1 cancels out
1 + 1 = 2
now we have 2x = 2
step 2 divide each side by 2
2x/2=x
2/2=1
we're left with x = 1
Now lets find ∠ZVW
∠ZVW and ∠ZXY happen to be opposite angles ( opposite angles are congruent )
This means that because ∠ZXY = 45 ∠ZVW also = 45
Now lets find ∠ZWV
∠ZWV and ∠XYZ happen to be opposite angles ( like stated previously, opposite angles are congruent)
So because ∠XYZ = 31 ∠ZWV also = 31
