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, \(4x - 9=101\)
\(4x=101 + 9\)
\(4x=110\)
\(x=\frac{110}{4}=27.5\)

Step2: Use consecutive angles property

Consecutive angles in a parallelogram are supplementary (\(sum = 180^{\circ}\)).
\((4z + 3)+101=180\)
\(4z+104 = 180\)
\(4z=180 - 104\)
\(4z=76\)
\(z = 19\)

Step3: Use opposite angles property again

\(2y+1=4z + 3\)
Substitute \(z = 19\)
\(2y+1=4\times19+3\)
\(2y+1=76 + 3\)
\(2y+1=79\)
\(2y=79 - 1\)
\(2y=78\)
\(y = 39\)

Answer:

\(x = 27.5\), \(y = 39\), \(z = 19\)