Question

find the measure of the three missing angles in the rhombus below. answer attempt 2 out of 4 $x = square$ $y = 127$ $z = square$

Explanation:

Step1: Recall rhombus angle - property

In a rhombus, opposite angles are equal.

Step2: Find angle \(x\)

Since the angle opposite to the \(127^{\circ}\) angle is \(x\), then \(x = 127^{\circ}\) because opposite angles of a rhombus are equal.

Step3: Use adjacent - angle property

Adjacent angles of a rhombus are supplementary (sum to \(180^{\circ}\)). Let's find \(z\). We know that \(z+127^{\circ}=180^{\circ}\).

Step4: Solve for \(z\)

Subtract \(127^{\circ}\) from both sides of the equation \(z + 127^{\circ}=180^{\circ}\), so \(z=180^{\circ}-127^{\circ}=53^{\circ}\).

Answer:

\(x = 127\), \(y = 127\), \(z = 53\)