Question

skill set #4.2 - properties of parallelograms
find the measure of the three missing angles in the rhombus below.

Explanation:

Step1: Use property of parallelogram (opposite angles equal)

In a parallelogram, opposite angles are equal. So \(x = y\) and \(z = 87^{\circ}\) (since \(z\) is opposite to \(87^{\circ}\) angle).

Step2: Use property of parallelogram (adjacent angles supplementary)

Adjacent angles in a parallelogram are supplementary (\(a + b=180^{\circ}\)). So \(x + 87^{\circ}=180^{\circ}\), then \(x = 180^{\circ}- 87^{\circ}=93^{\circ}\). Since \(x = y\), \(y = 93^{\circ}\)

Answer:

\(x = 93^{\circ}\), \(y = 93^{\circ}\), \(z = 87^{\circ}\)