Question

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

Explanation:

Step1: Use opposite - angles property

In a parallelogram, opposite angles are equal. So, $(x + 2)=(7y + 5)$ and $(x - 4)=z$. Also, adjacent angles are supplementary. Let's first use the fact that adjacent angles $(x + 2)$ and $(x - 4)$ are supplementary.
$(x + 2)+(x - 4)=180$

Step2: Solve the equation for x

Combine like - terms:
$x+2+x - 4=180$
$2x-2 = 180$
Add 2 to both sides:
$2x=180 + 2=182$
Divide both sides by 2:
$x=\frac{182}{2}=91$

Step3: Find the value of y

Substitute $x = 91$ into the equation $x + 2=7y+5$
$91+2=7y + 5$
$93=7y+5$
Subtract 5 from both sides:
$7y=93 - 5=88$
$y=\frac{88}{7}$

Step4: Find the value of z

Substitute $x = 91$ into the equation $z=x - 4$
$z=91-4=87$

Answer:

$x = 91$, $y=\frac{88}{7}$, $z = 87$