Question

in this parallelogram, find x, y, and z. after you enter your answer press go. x = y = z =

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal. So \(x = 82^{\circ}\) (since \(x\) and the \(82^{\circ}\) angle are opposite angles).

Step2: Use the property of consecutive angles in a parallelogram

Consecutive angles in a parallelogram are supplementary (\(x + y=180^{\circ}\)). Substitute \(x = 82^{\circ}\) into \(x + y=180^{\circ}\), we get \(y=180^{\circ}-82^{\circ}=98^{\circ}\).

Step3: Use the property of opposite angles in a parallelogram again

Since \(z\) and \(y\) are opposite angles, \(z = y\). So \(z = 98^{\circ}\).

Answer:

\(x = 82\), \(y = 98\), \(z = 98\)