Question

find the measure of the three missing angles in the rhombus below. answer attempt 1 out of 2 ( x = ) ( y = ) ( z = )

Explanation:

Step1: Properties of a rhombus

In a rhombus, opposite angles are equal. So, \(x = 95^{\circ}\) (since \(x\) is opposite to the \(95^{\circ}\) angle).

Step2: Sum of adjacent angles

The sum of adjacent angles in a rhombus is \(180^{\circ}\). Let's find \(y\). Since \(y\) is adjacent to the \(95^{\circ}\) angle, \(y=180 - 95\).

$$y = 85^{\circ}$$

Step3: Opposite angles property again

Since \(z\) is opposite to \(y\), \(z=y\). So, \(z = 85^{\circ}\)

Answer:

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