Question

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

Explanation:

Step1: Recall rhombus angle - properties

In a rhombus, opposite angles are equal and adjacent angles are supplementary (sum to 180°).

Step2: Find \(x\)

Since \(x\) is opposite to the 101° angle, \(x = 101^{\circ}\) because opposite angles of a rhombus are equal.

Step3: Find \(y\) and \(z\)

\(y\) and \(z\) are adjacent to the 101° angle. Let's find \(y\) (and \(z=y\) as opposite angles are equal). Using the supplementary - angle property, \(y+101^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-101^{\circ}=79^{\circ}\). And since \(z\) is opposite to \(y\), \(z = 79^{\circ}\).

Answer:

\(x = 101^{\circ}\), \(y = 79^{\circ}\), \(z = 79^{\circ}\)