Question

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

(image of a rhombus with one angle labeled 82°, and the other three angles labeled x°, y°, z°)

answer attempt 1 out of 2

x =

y =

z =

Explanation:

Step1: Recall properties of a rhombus

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

Step2: Find angle \(y\)

Since opposite angles in a rhombus are equal, the angle opposite to \(82^\circ\) is also \(82^\circ\). So \(y = 82^\circ\) (because \(y\) is opposite to the given \(82^\circ\) angle).

Step3: Find angle \(x\) and \(z\)

Adjacent angles in a rhombus are supplementary. So, if one angle is \(82^\circ\), the adjacent angle \(x\) (and \(z\), since \(x\) and \(z\) are opposite and equal) is \(180^\circ - 82^\circ\).
Calculating: \(180 - 82 = 98\). So \(x = 98^\circ\) and \(z = 98^\circ\) (since \(x\) and \(z\) are opposite angles in the rhombus, they are equal).

Answer:

\(x = \boldsymbol{98}\), \(y = \boldsymbol{82}\), \(z = \boldsymbol{98}\)