Question

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

answer

( x=square quad y=square quad z=square )

Explanation:

Step1: Use opposite angles property

In a parallelogram, opposite angles are equal. So, $5z + 1=- 8x + 7$. Also, $6y=8y - 5$.

Step2: Solve for $y$

For $6y=8y - 5$, subtract $6y$ from both sides: $0 = 2y-5$. Then add $5$ to both sides: $2y=5$, so $y = 10$.

Step3: Use consecutive angles property

Consecutive angles in a parallelogram are supplementary. So, $(5z + 1)+(8y - 5)=180$. Substitute $y = 10$: $(5z + 1)+(8\times10 - 5)=180$.
Simplify: $5z+1 + 75=180$, $5z+76 = 180$, $5z=104$, $z = 13$.

Step4: Solve for $x$

Substitute $z = 13$ into $5z + 1=- 8x + 7$. $5\times13+1=-8x + 7$, $65 + 1=-8x + 7$, $66=-8x + 7$, $-8x=59$, $x = 1$.

Answer:

$x = 1$, $y = 10$, $z = 13$