Question

quadrilateral tuvw is a kite. what is ( mangle t )? ( mangle t=) ( square^{circ} )

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \(360^{\circ}\). So, \(m\angle T + m\angle U+ m\angle V + m\angle W=360^{\circ}\).

Step2: Use the property of a kite

In a kite, one pair of opposite angles (the angles between the unequal sides) are equal. Here, \(\angle T\) and \(\angle V\) are equal (\(m\angle T = m\angle V\)). Let \(m\angle T=x\). Then the equation becomes \(x + 106^{\circ}+x + 92^{\circ}=360^{\circ}\).

Step3: Simplify the equation

Combine like - terms: \(2x+198^{\circ}=360^{\circ}\).
Subtract \(198^{\circ}\) from both sides: \(2x=360^{\circ}- 198^{\circ}\), so \(2x = 162^{\circ}\).

Step4: Solve for \(x\)

Divide both sides by 2: \(x=\frac{162^{\circ}}{2}=81^{\circ}\).

Answer:

\(81\)