Question

skill set #4.3 - properties of parallelograms (algebraic)
find the value of x, y, and z in the parallelogram below.

Explanation:

Step1: Use property of consecutive angles in parallelogram

In a parallelogram, consecutive angles are supplementary. So, \(85+(8x - 1)=180\)

$$
LATEXBLOCK0
$$

Step2: Use property of opposite angles in parallelogram

Opposite angles in a parallelogram are equal. So, \(-3z-4=85\)

$$
LATEXBLOCK1
$$

Also, \(-4y + 5=8x-1\). Substitute \(x = 12\)

$$
LATEXBLOCK2
$$

Answer:

\(x = 12\), \(y=-22.5\), \(z=-\frac{89}{3}\)