Question

find ( mangle u ) in rhombus ( rstu ).

Explanation:

Step1: Use the property of adjacent angles in a rhombus

In a rhombus, adjacent angles are supplementary. So, \((a - 2)+(2a-40)=180\).

Step2: Solve the equation for \(a\)

Combine like - terms: \(a+2a-2 - 40=180\), which simplifies to \(3a-42 = 180\).
Add \(42\) to both sides: \(3a=180 + 42\), so \(3a=222\).
Divide both sides by \(3\): \(a=\frac{222}{3}=74\).

Step3: Find \(m\angle U\)

Since \(m\angle U\) and \(m\angle S\) are adjacent angles in the rhombus, and \(m\angle S=2a - 40\), \(m\angle T=a - 2\). Also, \(m\angle U\) and \(m\angle T\) are supplementary.
First, find \(m\angle T\) by substituting \(a = 74\) into \(a-2\). So \(m\angle T=74 - 2=72^{\circ}\).
Since \(m\angle U+m\angle T = 180^{\circ}\) (adjacent angles in a rhombus are supplementary), then \(m\angle U=180-(a - 2)\). Substituting \(a = 74\), we get \(m\angle U=180-72\).

Answer:

\(108\)