Question

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

answer attempt 1 out of 2
x =
y =
z =
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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 \(x\)

The angle given is \(101^\circ\), and \(x\) is opposite to the angle adjacent to \(101^\circ\)? Wait, no. Wait, adjacent angles in a rhombus are supplementary. So the angle adjacent to \(101^\circ\) (let's say \(x\)) should satisfy \(x + 101^\circ= 180^\circ\). So \(x = 180 - 101 = 79^\circ\)? Wait, no, wait. Wait, in a rhombus, opposite angles are equal. So if one angle is \(101^\circ\), its opposite angle is also \(101^\circ\), and the other two opposite angles are equal and supplementary to \(101^\circ\). Wait, maybe I mixed up. Let's correct.

In a rhombus, opposite angles are equal. So if one angle is \(101^\circ\), then the angle opposite to it (let's say \(y\)) is also \(101^\circ\). Then the other two angles ( \(x\) and \(z\)) are equal and supplementary to \(101^\circ\). So \(x + 101^\circ= 180^\circ\), so \(x = 180 - 101 = 79^\circ\). Similarly, \(z\) is equal to \(x\) because they are opposite angles. So \(z = 79^\circ\), and \(y = 101^\circ\).

Wait, let's re-express:

1. Opposite angles in a rhombus are equal. So if the given angle is \(101^\circ\), then the angle opposite to it ( \(y\)) is also \(101^\circ\).

1. Adjacent angles in a rhombus are supplementary (sum to \(180^\circ\)). So the angle adjacent to \(101^\circ\) ( \(x\)) satisfies \(x + 101^\circ= 180^\circ\), so \(x = 180 - 101 = 79^\circ\).

1. Since \(x\) and \(z\) are opposite angles, they are equal. So \(z = x = 79^\circ\).

Step1: Determine \(x\)

Adjacent angles in rhombus are supplementary. So \(x + 101^\circ= 180^\circ\)
\(x = 180 - 101 = 79^\circ\)

Step2: Determine \(y\)

Opposite angles in rhombus are equal. So \(y = 101^\circ\) (since it's opposite to the \(101^\circ\) angle)

Step3: Determine \(z\)

Opposite angles in rhombus are equal. So \(z = x = 79^\circ\) (since \(x\) and \(z\) are opposite angles)

Answer:

\(x = 79\), \(y = 101\), \(z = 79\)