Question

find the measure of the three missing angles in the parallelogram below.
answer attempt 2 out of 2
$x = square$ $y = square$ $z = square$

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal. So \(x = 95^{\circ}\) because \(x\) and the \(95^{\circ}\) angle are opposite angles.

Step2: Use the property of consecutive angles in a parallelogram

Consecutive angles in a parallelogram are supplementary (sum to \(180^{\circ}\)). Since \(x\) and \(y\) are consecutive angles, \(x + y=180^{\circ}\). Substituting \(x = 95^{\circ}\), we get \(95^{\circ}+y = 180^{\circ}\), then \(y=180^{\circ}- 95^{\circ}=85^{\circ}\).

Step3: Use the property of opposite angles again

Since \(z\) and \(y\) are opposite angles in the parallelogram, \(z = y\). So \(z = 85^{\circ}\).

Answer:

\(x = 95\), \(y = 85\), \(z = 85\)