Question

Find the value of x,y, and z in the parallelogram below.x = y =z =

Answer 1

One of the properties of parallelograms is opposite angles are congruent.

It means:

$\begin{gathered} 100=-y-5\text{ Equation 1} \\ \text{And} \\ 4x+4=4z+8\text{ Equation 2} \end{gathered}$

We can solve for y in equation 1:

$\begin{gathered} \text{Add y to both sides} \\ 100+y=-y-5+y \\ 100+y=-5 \\ \text{Subtract 100 from both sides} \\ 100+y-100=-5-100 \\ y=-105\degree \end{gathered}$

Another property of parallelograms is adjacent angles add up to 180°.

It means:

$100+(4z+8)=180$

Then, we can solve for z:

$\begin{gathered} \text{Subtract 108 from both sides} \\ 100+4z+8-108=180-108 \\ 108+4z-108=72 \\ 4z=72 \\ \text{Divide both sides by 4} \\ \frac{4z}{4}=\frac{72}{4} \\ z=18\degree \end{gathered}$

Now, we can replace z into equation 2 and solve for x:

$\begin{gathered} 4x+4=4\cdot18+8 \\ 4x+4=72+8 \\ 4x+4=80 \\ \text{Subtract 4 from both sides} \\ 4x+4-4=80-4 \\ 4x=76 \\ \text{Divide both sides by 4} \\ \frac{4x}{4}=\frac{76}{4} \\ x=19\degree \end{gathered}$

The answer is: x=19°, y=-105°, z