Question

find ( mangle t ) in rhombus ( tuvw ).

Explanation:

Step1: Use the property of adjacent angles in a rhombus

In a rhombus, adjacent angles are supplementary. So, \((7a - 35)+(6a + 46)=180\).

Step2: Solve the equation for \(a\)

Combine like - terms: \(7a+6a-35 + 46=180\), which simplifies to \(13a+11 = 180\).
Subtract \(11\) from both sides: \(13a=180 - 11=169\).
Divide both sides by \(13\): \(a=\frac{169}{13}=13\).

Step3: Find the measure of \(\angle U\)

Substitute \(a = 13\) into the expression for \(\angle U\): \(\angle U=7a-35=7\times13 - 35=91 - 35 = 56^{\circ}\).

Step4: Use the property of opposite angles in a rhombus

In a rhombus, \(\angle T\) and \(\angle V\) are equal, and \(\angle U\) and \(\angle W\) are equal. Also, since \(\angle T+\angle U = 180^{\circ}\) (adjacent angles are supplementary).
So, \(m\angle T=180 - m\angle U\).
Since \(m\angle U = 56^{\circ}\), then \(m\angle T=180-56 = 124^{\circ}\).

Answer:

\(124^{\circ}\)