Question

find the value of x, y, and z in the parallelogram below.
answer attempt 2 out of 2
x = y = z =

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal.
So, \(-4x - 1=75\)
\(-4x=75 + 1\)
\(-4x=76\)
\(x=\frac{76}{-4}=-19\)

Step2: Use the property of consecutive angles in a parallelogram

Consecutive angles in a parallelogram are supplementary (\(sum = 180^{\circ}\)).
So, \(-y-10 + 75=180\)
\(-y+65 = 180\)
\(-y=180 - 65\)
\(-y=115\)
\(y=-115\)

Step3: Use the property of opposite angles in a parallelogram

Since \(4z-3=-y - 10\), substitute \(y=-115\)
\(4z-3=-(-115)-10\)
\(4z-3=115 - 10\)
\(4z-3=105\)
\(4z=105 + 3\)
\(4z=108\)
\(z=\frac{108}{4}=27\)

Answer:

\(x=-19\), \(y = - 115\), \(z = 27\)