Question

find the measure of the three missing angles in the rhombus below.

(image of a rhombus with one angle labeled 58°, and the other three angles labeled x°, y°, z°)

answer attempt 1 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 \(180^\circ\)).

Step2: Find \(z\)

Since opposite angles in a rhombus are equal, the angle opposite to \(58^\circ\) (which is \(z^\circ\)) is equal to \(58^\circ\). So \(z = 58\).

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

Adjacent angles to \(58^\circ\) (like \(x\) and \(y\)) are supplementary to \(58^\circ\). So \(x = 180 - 58 = 122\) and \(y = 122\) (since opposite angles in a rhombus are equal, \(x\) and \(y\) are opposite to each other, so they are equal).

Answer:

\(x = 122\), \(y = 122\), \(z = 58\)